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 X X 1 1 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 (a+1)X aX aX 0 X X X aX 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 X X 0 aX aX aX
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 0 (a+1)X X (a+1)X (a+1)X X (a+1)X X X
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 X (a+1)X 0 aX 0 0 (a+1)X 0 X
generates a code of length 31 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 80.
Homogenous weight enumerator: w(x)=1x^0+93x^80+186x^84+192x^87+183x^88+1152x^91+117x^92+1728x^95+147x^96+105x^100+78x^104+63x^108+39x^112+9x^116+3x^120
The gray image is a linear code over GF(4) with n=124, k=6 and d=80.
This code was found by Heurico 1.16 in 0.0797 seconds.