The generator matrix

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

generates a code of length 32 over F4[X]/(X^2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+519x^88+1038x^92+1035x^96+972x^100+510x^104+6x^108+15x^120

The gray image is a linear code over GF(4) with n=128, k=6 and d=88.
This code was found by Heurico 1.16 in 0.0649 seconds.