The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1
0 X 0 0 0 0 X X X aX 0 X (a+1)X aX X aX aX X (a+1)X X (a+1)X X 0 (a+1)X (a+1)X X aX aX (a+1)X 0 X aX 0
0 0 X 0 0 X (a+1)X aX aX aX 0 0 aX aX 0 aX (a+1)X aX 0 X aX aX X (a+1)X X (a+1)X 0 X aX (a+1)X 0 X (a+1)X
0 0 0 X 0 (a+1)X 0 X aX (a+1)X X X X 0 X (a+1)X (a+1)X X 0 X aX (a+1)X (a+1)X 0 aX 0 aX aX 0 X (a+1)X aX (a+1)X
0 0 0 0 X X X (a+1)X X X X aX 0 0 0 aX (a+1)X aX X 0 0 X aX aX 0 aX aX X (a+1)X (a+1)X X (a+1)X aX
generates a code of length 33 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 88.
Homogenous weight enumerator: w(x)=1x^0+225x^88+165x^92+921x^96+2382x^100+165x^104+78x^108+75x^112+54x^116+18x^120+9x^124+3x^128
The gray image is a linear code over GF(4) with n=132, k=6 and d=88.
This code was found by Heurico 1.16 in 96.5 seconds.