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.