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
0 X 0 0 0 0 X X X aX aX (a+1)X 0 0 X aX aX X X 0 X aX aX 0 0 X
0 0 X 0 0 X (a+1)X (a+1)X aX 0 (a+1)X 0 aX X X (a+1)X aX 0 aX (a+1)X (a+1)X 0 0 X aX (a+1)X
0 0 0 X 0 (a+1)X 0 (a+1)X X aX (a+1)X aX (a+1)X (a+1)X (a+1)X 0 aX aX X 0 0 (a+1)X 0 X (a+1)X X
0 0 0 0 X X X (a+1)X (a+1)X (a+1)X aX X (a+1)X (a+1)X (a+1)X (a+1)X aX 0 0 X aX X X (a+1)X aX (a+1)X
generates a code of length 26 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 64.
Homogenous weight enumerator: w(x)=1x^0+48x^64+159x^68+162x^72+174x^76+3072x^78+150x^80+135x^84+105x^88+48x^92+27x^96+12x^100+3x^104
The gray image is a linear code over GF(4) with n=104, k=6 and d=64.
This code was found by Heurico 1.16 in 0.0619 seconds.