The generator matrix

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

generates a code of length 33 over F4[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+108x^84+24x^85+168x^86+804x^87+972x^88+360x^89+660x^90+2640x^91+2361x^92+1200x^93+1572x^94+5256x^95+4233x^96+2640x^97+2760x^98+8736x^99+5946x^100+3384x^101+2544x^102+7476x^103+4470x^104+1608x^105+1380x^106+2736x^107+1218x^108+132x^110+66x^112+54x^116+18x^120+9x^124

The gray image is a linear code over GF(4) with n=132, k=8 and d=84.
This code was found by Heurico 1.16 in 8.22 seconds.