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

generates a code of length 25 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+30x^72+192x^75+18x^76+9x^80+3x^84+3x^100

The gray image is a linear code over GF(4) with n=100, k=4 and d=72.
This code was found by Heurico 1.16 in 1.01e-007 seconds.