The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  1  1  X  X  X  1  1  1  1  X  X  X  1  1  1  1 2X+2 2X+2 2X+2  X  X  X  X  X  1  1 2X+2 2X+2 2X+2  1  X  X 2X 2X 2X  X  0  0  0 2X+2  X  X  1  1  1  1  1  1
 0 2X  0 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0  0 2X 2X  0 2X  0  0 2X 2X  0 2X 2X  0 2X  0 2X  0 2X  0  0 2X  0  0
 0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0  0 2X 2X  0 2X 2X  0 2X 2X  0 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X  0  0

generates a code of length 77 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+32x^77+18x^78+6x^79+1x^80+1x^82+2x^83+2x^84+1x^90

The gray image is a code over GF(2) with n=616, k=6 and d=308.
This code was found by Heurico 1.16 in 0.281 seconds.