The generator matrix

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

generates a code of length 33 over F4[X]/(X^2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+312x^86+264x^87+807x^88+1068x^89+1632x^90+1380x^91+2055x^92+2556x^93+3156x^94+2880x^95+3519x^96+3984x^97+4860x^98+4056x^99+4932x^100+5808x^101+5388x^102+4056x^103+4194x^104+3108x^105+2676x^106+1188x^107+855x^108+372x^109+408x^110+12x^112+6x^116+3x^120

The gray image is a linear code over GF(4) with n=132, k=8 and d=86.
This code was found by Heurico 1.16 in 8.07 seconds.