Unfortunately GCT has not been updated for long time and it works only with original version of eTPU Function Selector (containing function sets based on ByteCraft compiler).
Newer CW eTPU Function Selector (containing CW based function sets) does not work with GCT and gct.c and gct.h files must be hand written.
If you want to use original function set with MPC5777C or and GCT, you can use option "Generic CPU with eTPU2".
I have such example code here (for MPC5746R):
https://community.nxp.com/t5/MPC5xxx-Knowledge-Base/Example-MPC5746R-eTPU-original-set1-integration-...