The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1  X  1  1  1  X  1  1
 0  X  0  0  0  0  0  X  X  X  X a*X  X a^2*X a^2*X a^2*X  X a^2*X  X  X  X  X a*X a^2*X a*X  0 a^2*X a^2*X  0  X  X  0
 0  0  X  0  0  0  X a^2*X a^2*X  X a*X a*X a*X  0 a*X a^2*X a*X a*X a^2*X  X  0 a^2*X  0  X a^2*X  X a*X  0 a*X  0  X  0
 0  0  0  X  0  0 a^2*X  X  0 a*X a*X a*X  0 a^2*X  X a*X  X a*X  0  X a^2*X a^2*X a^2*X a^2*X  0  X a*X  X  0 a^2*X a*X  0
 0  0  0  0  X  0  X a^2*X a*X  0  X a^2*X a^2*X  X  0 a^2*X  0 a*X  X  X a*X a*X  X a*X a^2*X a*X a^2*X a^2*X a^2*X  0  X  0
 0  0  0  0  0  X a^2*X  X a^2*X  X a^2*X  X a*X a^2*X  X  0 a*X a*X  X a*X  X a*X  0 a^2*X a*X a*X  X  X a^2*X a*X  X  0

generates a code of length 32 over F4[X]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+90x^76+312x^80+435x^84+1035x^88+3048x^92+5724x^96+4476x^100+555x^104+402x^108+195x^112+93x^116+18x^120

The gray image is a linear code over GF(4) with n=128, k=7 and d=76.
This code was found by Heurico 1.16 in 1.15 seconds.