The generator matrix

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

generates a code of length 33 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+105x^80+354x^84+414x^88+192x^90+483x^92+1728x^94+540x^96+5184x^98+567x^100+5184x^102+501x^104+525x^108+366x^112+171x^116+57x^120+12x^124

The gray image is a linear code over GF(4) with n=132, k=7 and d=80.
This code was found by Heurico 1.16 in 1.23 seconds.