The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  1  1 aX  1  1  1  X aX  1  1  1  1  1  1  1  1  1  1 (a+1)X  1  1  1  0  1  1
 0  1  0  0  X aX (a+1)X  X (a+1)X (a+1)X+1  a  1 aX+a  1 X+1 X+a+1 (a+1)X+1  1  1 X+1 aX+1 aX+a+1 X+a aX+a aX+1 (a+1)X+1  a aX+1  a  1 aX aX (a+1)X  1 aX  1
 0  0  1  0 (a+1)X+1 (a+1)X (a+1)X  a  0 a+1 X+a+1 X+1 (a+1)X+a (a+1)X+a aX+a aX+a+1 (a+1)X+a+1 aX+a+1  X X+1 aX (a+1)X+1 aX+1 aX (a+1)X+1 (a+1)X aX+a+1 a+1 aX+a (a+1)X a+1 aX+1 X+1  a aX X+a+1
 0  0  0  1 a+1  1  a X+a+1 aX+a+1 (a+1)X+a+1 (a+1)X+a+1 (a+1)X+a X+1 X+a  a aX+a (a+1)X+a aX+a+1 aX+a+1 aX+a+1 (a+1)X (a+1)X+1 a+1  1 aX aX+a+1  a  1 X+a+1  1 X+a+1  0 aX+1 X+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+2049x^96+7188x^100+12480x^104+18744x^108+17706x^112+6804x^116+552x^120+12x^128

The gray image is a linear code over GF(4) with n=144, k=8 and d=96.
This code was found by Heurico 1.16 in 75.3 seconds.