The generator matrix

 1  0  0  0  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  X  1  0  1  1  1  1  X (a+1)X  1 aX
 0  1  0  0  0  X  X (a+1)X+1 aX+1  1 aX+a a+1 X+a (a+1)X+a+1  0  1  X aX+a+1  a X+1  1  a aX X+1  1 (a+1)X+a+1 X+a  1 a+1  1  1 aX+1 aX
 0  0  1  0  1 (a+1)X+a (a+1)X+a+1  X aX+a aX+a aX  0 aX+a+1 aX+1  0 a+1 X+a a+1 X+a aX+a (a+1)X+a+1  X  1 (a+1)X+a X+a+1 (a+1)X+1 (a+1)X+a aX+1  a X+1 (a+1)X+1  1  X
 0  0  0  1 a+1  a  1 (a+1)X+a aX (a+1)X+a (a+1)X+1 X+a+1  a aX+a  a  0 aX (a+1)X+a a+1  1 (a+1)X+1 X+a+1 a+1 aX+a aX aX+a+1 X+1 a+1 (a+1)X+a+1 X+a+1  X aX+a  1
 0  0  0  0  X  0 aX  0  0  0 aX  X aX  X (a+1)X aX  X (a+1)X  0 aX (a+1)X (a+1)X aX aX  X  0 (a+1)X  0 (a+1)X (a+1)X  0 aX  X

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

Homogenous weight enumerator: w(x)=1x^0+228x^83+795x^84+252x^85+1776x^86+1944x^87+3330x^88+1188x^89+5400x^90+6072x^91+10431x^92+3192x^93+11868x^94+14916x^95+20028x^96+6648x^97+21264x^98+23556x^99+29433x^100+8604x^101+21672x^102+20496x^103+20874x^104+4068x^105+10488x^106+6240x^107+5097x^108+624x^109+1260x^110+276x^111+66x^112+24x^116+12x^120+12x^124+9x^128

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 102 seconds.