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

generates a code of length 32 over F4[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+156x^84+348x^88+801x^92+1422x^96+1071x^100+108x^104+102x^108+51x^112+27x^116+6x^120+3x^124

The gray image is a linear code over GF(4) with n=128, k=6 and d=84.
This code was found by Heurico 1.16 in 0.173 seconds.