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

generates a code of length 36 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+162x^96+174x^100+174x^104+768x^105+147x^108+2304x^109+102x^112+72x^116+66x^120+66x^124+39x^128+18x^132+3x^140

The gray image is a linear code over GF(4) with n=144, k=6 and d=96.
This code was found by Heurico 1.16 in 0.301 seconds.