The generator matrix

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

generates a code of length 32 over F4[X]/(X^2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+96x^82+348x^83+780x^84+120x^85+1116x^86+1416x^87+2280x^88+480x^89+2172x^90+3048x^91+4185x^92+1680x^93+5112x^94+5136x^95+6798x^96+2400x^97+6264x^98+5676x^99+6204x^100+1464x^101+3372x^102+2568x^103+2094x^104+300x^106+240x^107+81x^108+63x^112+30x^116+12x^120

The gray image is a linear code over GF(4) with n=128, k=8 and d=82.
This code was found by Heurico 1.16 in 92.8 seconds.