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 X 1 X 1 1 1 X
0 X 0 0 0 0 X X X aX 0 X (a+1)X aX (a+1)X aX X X aX 0 (a+1)X X X (a+1)X 0 (a+1)X (a+1)X X (a+1)X 0 (a+1)X X 0 0 X (a+1)X X aX X X X
0 0 X 0 0 X (a+1)X aX aX aX 0 0 aX aX 0 aX (a+1)X aX (a+1)X (a+1)X aX 0 (a+1)X 0 (a+1)X (a+1)X aX X X (a+1)X (a+1)X aX (a+1)X (a+1)X X aX 0 0 (a+1)X aX (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 X X (a+1)X (a+1)X (a+1)X 0 0 (a+1)X (a+1)X 0 aX X aX 0 X (a+1)X aX 0 (a+1)X (a+1)X 0 (a+1)X (a+1)X 0 (a+1)X
0 0 0 0 X X X (a+1)X X X X aX 0 0 0 aX X aX (a+1)X (a+1)X 0 X aX aX aX aX aX 0 0 X X X X (a+1)X X (a+1)X (a+1)X 0 aX X X
generates a code of length 41 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 112.
Homogenous weight enumerator: w(x)=1x^0+321x^112+48x^114+432x^118+297x^120+1296x^122+1296x^126+189x^128+126x^136+81x^144+9x^152
The gray image is a linear code over GF(4) with n=164, k=6 and d=112.
This code was found by Heurico 1.16 in 3.62 seconds.