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

generates a code of length 34 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+72x^88+177x^92+351x^96+1296x^100+1869x^104+114x^108+84x^112+63x^116+33x^120+27x^124+6x^128+3x^132

The gray image is a linear code over GF(4) with n=136, k=6 and d=88.
This code was found by Heurico 1.16 in 0.089 seconds.