The generator matrix

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

generates a code of length 32 over F4[X]/(X^2) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+300x^83+390x^84+432x^85+1056x^86+1620x^87+2181x^88+1452x^89+1908x^90+3120x^91+3954x^92+2928x^93+3360x^94+4776x^95+6750x^96+3864x^97+4536x^98+5628x^99+5982x^100+3168x^101+2496x^102+2724x^103+1698x^104+444x^105+468x^106+264x^107+18x^108+15x^112+3x^120

The gray image is a linear code over GF(4) with n=128, k=8 and d=83.
This code was found by Heurico 1.16 in 7.31 seconds.