The generator matrix
1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 X 1 1 1 (a+1)X 1 1
0 1 1 a (a+1)X+a+1 0 (a+1)X+1 a (a+1)X+a+1 1 0 a (a+1)X+1 1 X X (a+1)X+a+1 X+a 1 aX+a aX+a+1 (a+1)X+1 1 aX+a+1 aX+1
0 0 (a+1)X 0 X X (a+1)X X (a+1)X X 0 0 X X aX 0 (a+1)X 0 aX aX aX aX 0 X X
0 0 0 X aX X aX (a+1)X (a+1)X 0 X (a+1)X 0 aX X aX aX 0 0 (a+1)X aX 0 (a+1)X (a+1)X X
generates a code of length 25 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 68.
Homogenous weight enumerator: w(x)=1x^0+594x^68+918x^72+1569x^76+969x^80+24x^84+21x^92
The gray image is a linear code over GF(4) with n=100, k=6 and d=68.
This code was found by Heurico 1.16 in 0.338 seconds.