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

generates a code of length 36 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 100.

Homogenous weight enumerator: w(x)=1x^0+69x^100+264x^104+372x^108+282x^112+12x^116+9x^120+3x^128+3x^132+9x^136

The gray image is a linear code over GF(4) with n=144, k=5 and d=100.
This code was found by Heurico 1.16 in 0.015 seconds.