The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  X  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1
 0  1  1  a a^2  0 a^2*X+1 a^2*X+a^2  a  1  0 a^2*X+1  a  1 a^2*X+a^2 X+a  1 a^2*X+1  0 a^2*X+a^2 a^2*X+a^2  a  X X+a  1 a^2*X X+a^2 a^2 a*X a^2*X+a^2  0 a^2*X+1
 0  0 a^2*X  0  0  0  X  X  X  X  X  X a^2*X a^2*X a*X a^2*X a^2*X  0 a^2*X a*X a^2*X  0  X  X a*X a^2*X a^2*X a^2*X a^2*X  X  0  X
 0  0  0  X  0  X a^2*X  0  X a^2*X  X  0 a*X a^2*X  0  0  X a*X  X  0 a^2*X  X a*X  X a^2*X a*X  X a^2*X a*X  0  0 a^2*X
 0  0  0  0 a^2*X a^2*X  X a^2*X a*X  0 a^2*X  X  X a*X  X  X  X  0  0 a*X  0 a*X a^2*X  X a*X a*X a*X  X  X  X a^2*X a*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+312x^84+96x^85+156x^86+864x^88+576x^89+336x^90+1182x^92+1536x^93+936x^94+2112x^96+2496x^97+1104x^98+1848x^100+1440x^101+540x^102+675x^104+84x^108+51x^112+24x^116+9x^120+6x^124

The gray image is a linear code over GF(4) with n=128, k=7 and d=84.
This code was found by Heurico 1.16 in 38.8 seconds.