The generator matrix

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

generates a code of length 25 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+141x^64+234x^68+924x^72+2406x^76+156x^80+102x^84+84x^88+42x^92+6x^96

The gray image is a linear code over GF(4) with n=100, k=6 and d=64.
This code was found by Heurico 1.16 in 5.84 seconds.