Hi, grey code is unlike binary, in that only one digit changes at once.
With binary the next step from 00111 is 01000 i.e. 4 digits change over.
The OP said..
Yesterday I was alerted by a helpful ATCO that my mode C was returning erratic altitudes ranging between FL11 and 4500ft when actually I was level at 1300ft.
So there are three altitudes mentioned, therefore there is more than one loose connection in the grey-code cables. Try lots of switch cleaner...!