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

generates a code of length 76 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+60x^75+175x^76+15x^80+4x^91+1x^92

The gray image is a code over GF(2) with n=608, k=8 and d=300.
This code was found by Heurico 1.16 in 0.485 seconds.