Error codes 2A77 and 2A3F causing limp mode?

2a3f. Insufficient voltage to valve-tronic motor can cause the engine to run poorly or not at all. So, it must have cooked the power distrubution /supply wire to the motor. Id check that for ohms and continuity first" . If its bad replace it. But its tricky becuas you gotta find the 2 ends of it and test there. End to end. Hope this helps good luck.

So chances of both sensors going out at the same time is a possibility but I have seen the DME go out as well.

2A77 - Oxygen sensor after catalytic converter, signal response too slow (bank 2)
2A3F - Oxygen sensor before catalytic converter, signal response too slow (bank 2)

If you change the sensors out and you get the same codes, I would get a preprogrammed DME which should fix it. Here is the location of the DME so you can swap it out in case you need it. Check out the images (below). Let us know how it goes.

And the 2a77 code is most likely related to the same problem if you fix it chances are it would take care of both codes and solve your problem. Good luck fingers crossed.

2a77 and 2a3f are Bmw specific codes. Power supply issues /damaged. So yeah
Check the power supply circuit