The generator matrix

 1  0  1  1  1  1  1  1  1  0  0  1  1  1  1  0  1  0  X  1  1  1  1 (a+1)X  1
 0  1  1  a a+1  0 (a+1)X+1  a (a+1)X+a+1  1  1  0 (a+1)X+a+1 (a+1)X+1 (a+1)X+a+1  1 (a+1)X+1  1  1  0  0  a  a  1  0
 0  0 (a+1)X  0  0  0  0  X aX  X  X  X (a+1)X (a+1)X (a+1)X aX (a+1)X  0 aX  0  X aX  0  0  0
 0  0  0  X  0  0  X (a+1)X (a+1)X aX (a+1)X (a+1)X (a+1)X (a+1)X (a+1)X (a+1)X (a+1)X aX (a+1)X aX aX aX aX aX  0
 0  0  0  0 (a+1)X  0 aX  0  X  X (a+1)X aX  X aX aX (a+1)X  X (a+1)X aX  0  0 aX  0 aX  0
 0  0  0  0  0  X aX  X aX aX aX  0  0  0  X aX (a+1)X  X  X aX aX aX (a+1)X aX  X

generates a code of length 25 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+84x^56+12x^57+288x^60+144x^61+204x^62+144x^63+384x^64+684x^65+612x^66+1728x^67+504x^68+1728x^69+2232x^70+7776x^71+522x^72+2916x^73+3720x^74+15552x^75+636x^76+3888x^77+3900x^78+11664x^79+684x^80+2916x^81+1620x^82+576x^84+282x^88+108x^92+27x^96

The gray image is a linear code over GF(4) with n=100, k=8 and d=56.
This code was found by Heurico 1.16 in 6.13 seconds.