[Architex_mA8tey]

Here are the ross tech wiki outputs for those codes -

17118/P0734/001844 - Gear 4: Incorrect Ratio

Possible Symptoms
Clutch Slipping
Reduced Power Output

Possible Causes
Gear related Clutch slipping/faulty
Gear related Solenoid Valve dirty/faulty
Overloaded Clutch due to continuous high Torque or Tuning
Wiring and/or Connections faulty
Sensor Gear Position Indicator faulty
Mechanical Failure

Possible Solutions
Check Engine Values for Plausibility, especially Torque related ones.
Check Wiring and Connections
Check Sensor Gear Position Indicator
Check Gear Solenoides

Special Notes
The gear monitoring of the transmission control module checks the gear ratio by comparing transmission input and output speed in regard of the currently selected gear. This fault code is being set when recognizing an implausible transmission ratio.


17114/P0730/001840 - Gear Ratio Monitoring: Incorrect Gear Ratio

Possible Symptoms
Malfunction Indicator Light (MIL) ON

Possible Causes
Transmission Fluid contaminated
Transmission faulty (Mechanical Problem)

Possible Solutions
Check Transmission Fluid (Color and Contamination)
Replace Transmission Fluid when necessary
Check Transmission Mechanics

Special Notes
Transmission Damage may be caused by Engine Problems, make sure there are no other/relevant Fault Codes stored in Engine Control Module.
When found in 6-Speed Automatic Transmission (01J/Multitronic):
Instructions on how to check the Transmission Fluid as well as Details on a special Test Kit can be found in TPI 2016661. TPI 2006088 may also be relevant.
A conversion from 6 to 7 Clutch Plates may be possible. See TPI 2004856 for Details.


17087/P0703/001795 - Brake Switch (F): Electrical Malfunction

Possible Symptoms
Malfunction Indicator Light (MIL) ON

Possible Causes
Wiring and/or Connector(s) from/to Brake Switch (F) faulty
Brake Switch (F) faulty

Possible Solutions
Check Wiring and/or Connector(s) from/to Brake Switch (F)
Check/Replace Brake Switch (F)

Special Notes
When found in Vehicles with Drive-by-Cable (DBC) the Brake Switch (F) is connected to the Transmission Control Module. On older Models this Code is stored automatically after Terminal 15/Ignition is switched ON. If the Brake Switch (F) is OK you can avoid this Fault Code by pressing the Brake Pedal after switching on the Ignition and prior to checking Fault Codes. The Code should automatically be cleared then.
When found in Vehicles with Drive-by-Wire (DBW) the Brake Switch (F) is connected to the Engine Control Module In this case you should check the Engine Control Module for Fault Codes as well and the Data Bus Wiring between Engine and Transmission Control Module.


65535 - Internal Control Module Memory Error

Possible Causes
Control Module housing leaky > Control Module wet
Wiring from/to Control Module faulty
Control Module faulty

Possible Solutions
Check/Clean Wiring from/to Control Module
Replace Control Module

Special Notes
This fault is NOT to be ignored when found in a major and/or critical system (Airbag, ABS etc.).
When stored in other unimportant systems (Radio etc.) the general suggestion is to ignore it unless you notice functional limitations. Within the warranty period dealers are usually required to replace such control modules, but there have been a couple of cases with similar codes where these are getting ignored due to flaws in the control module software. If in doubt please refer to technical bulletins and similar documents provided by the vehicle manufacturer.
Audi Airbag 6 & 7
Problem: A fault of the acceleration sensor may result in the above fault.
Solution: Replace Airbag control module and both acceleration sensors.
Audi Airbag 8
Problem: Due to under voltage the control module does not complete it's self test successfully.
Solution: Replace Airbag control module and install a under voltage protection relay for it.
Certain older TDI ECUs which have a vacuum line going to them
Problem: Vacuum line broken, either before ECU or inside ECU.
Solution: Inspect and repair vacuum lines to ECU and inside ECU.


17114/P0730/001840 - Gear Ratio Monitoring: Incorrect Gear Ratio

Possible Symptoms
Malfunction Indicator Light (MIL) ON

Possible Causes
Transmission Fluid contaminated
Transmission faulty (Mechanical Problem)

Possible Solutions
Check Transmission Fluid (Color and Contamination)
Replace Transmission Fluid when necessary
Check Transmission Mechanics

Special Notes
Transmission Damage may be caused by Engine Problems, make sure there are no other/relevant Fault Codes stored in Engine Control Module.
When found in 6-Speed Automatic Transmission (01J/Multitronic):
Instructions on how to check the Transmission Fluid as well as Details on a special Test Kit can be found in TPI 2016661. TPI 2006088 may also be relevant.
A conversion from 6 to 7 Clutch Plates may be possible. See TPI 2004856 for Details.


I have to say it doesn't look good - 4th gear was what went on my recently failed box
If it is that then your only hope is for a rebuild or a service exchange box, or talk to A8 parts to see if they have any reasonable ones there.
Good luck with things . . . .