The generator matrix

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

generates a code of length 32 over F4[X]/(X^2) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+264x^89+228x^90+144x^91+324x^92+600x^93+348x^94+252x^95+288x^96+384x^97+60x^98+72x^99+93x^100+264x^101+324x^102+108x^103+123x^104+216x^105+3x^108

The gray image is a linear code over GF(4) with n=128, k=6 and d=89.
This code was found by Heurico 1.16 in 0.031 seconds.