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

generates a code of length 37 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+51x^96+165x^100+162x^104+960x^108+2403x^112+99x^116+66x^120+81x^124+54x^128+36x^132+12x^136+3x^140+3x^144

The gray image is a linear code over GF(4) with n=148, k=6 and d=96.
This code was found by Heurico 1.16 in 0.0988 seconds.