If you write the integers in order in base -2, and convert them using the "shift and exclusive or" that converts to Gray from straight binary, you get a Gray code. The 3-bit Gray code has indexes that range over the 3-bit base -2 numbers, namely -2 to 5. Similarly, the 4-bit Gray code corresponding to 4-bit base -2 numbers has indexes ranging from -10 to 5. It is not a reflected Gray code, but it almost is. The 4-bit Gray code can be generated by starting with 0 and 1, reflecting this about a horizontal axis at the top of the list, and then reflecting it about a horizontal axis at the bottom of the list, and so on. It is cyclic.
To convert back to base -2 from this Gray code, the rules are of course the same as they are for converting to straight binary from ordinary reflected binary Gray code (because these operations are inverses, no matter what the interpretation of the bit strings is).