The generator matrix

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

generates a code of length 32 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+399x^88+1032x^92+1215x^96+1116x^100+300x^104+12x^108+12x^112+9x^120

The gray image is a linear code over GF(4) with n=128, k=6 and d=88.
This code was found by Heurico 1.16 in 0.173 seconds.