What advantages do the absolute encoders gain by employing Gray code transmission instead of binary code?
Imagine the encoder is a 12-bit encoder sitting right at the mid-scale transition between 0x7FF and 0x800. If the inner workings of the encoder consist of something like a code wheel with 12 independent photodiodes, all 12 bits would have to change at once, for a negligible movement. Since there are mechanical tolerances, some of the bits would change before others and there would be a lot of confusion at that particular angle. The same problem exists at every other position where more than one bit changes at a time. 

Using a Gray code for the code wheel completely eliminates that problem provided that the tolerances don't exceed a fraction of an LSB since only one bit changes at a time, and worst case your negligible motion results in a change equal to the resolution of the encoder. 

Modern high resolution encoders can use other methods (such as a very fast camera reading a coded strip) and take care of sampling properly so you always get a result that makes sense.