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

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+66x^68+267x^72+624x^76+21x^80+18x^84+9x^88+12x^92+6x^96

The gray image is a linear code over GF(4) with n=100, k=5 and d=68.
This code was found by Heurico 1.16 in 0.015 seconds.