I had the same problem. Its probably the passenger side engine mount. On the later TDi's the mount has a solenoid which controls the rigidity of the mount..
the way the mounts work is that there is a fluid chamber with a plastic body in the middle of it, with small channel cut through it. this allows fluid from the top chamber, through the plastic body, to the bottom chamber. the bottom chamber is rubber lined and can deform under pressure. there is also an airway vented to atmosphere, with a rubber membrane separating the fluid from the atmosphere. a solenoid valve, controlled by the motronic, can open or close the airway.
below 1100 rpm (i.e idle), the engine vibrations are not enough to force fluid from the top chamber, through the passageway to the bottom chamber. the airway is open (solenoid valve open). the rubber membrane creates a soft cushion which absorbs the high frequency vibrations.
above 1100 rpm the soleniod valve is closed which blocks the airway and so "hardens" the mount (the fluid has nowhere to go). thus the mount is effectively solid.
the high frequency vibrations at speed are absorbed by the membrane (as in the idle case), while the more damaging low frequency vibrations cause the fluid to force itself through the chamber in the plastic body to the lower chamber, forcing the (lower) rubber chamber to distort - effectively absorbing the vibrations.
in this case i would suspect that the mounts are bad - possibly as simple as the connectors have been pulled off.
I just took the solenoid mount out and replaced it with a standard non electric mount. I think a new mount is about £75 + vat from audi... try the connection 1st, you will see it on mount..
