The generator matrix

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

generates a code of length 33 over F4[X]/(X^2) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+228x^83+504x^84+780x^85+900x^86+2400x^87+3003x^88+3720x^89+3180x^90+6588x^91+8184x^92+8592x^93+7260x^94+15216x^95+16440x^96+18192x^97+11784x^98+26892x^99+22179x^100+22380x^101+13260x^102+20880x^103+17052x^104+11976x^105+6060x^106+7380x^107+4173x^108+1944x^109+564x^110+288x^111+81x^112+36x^116+15x^120+9x^124+3x^132

The gray image is a linear code over GF(4) with n=132, k=9 and d=83.
This code was found by Heurico 1.16 in 99.6 seconds.