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

generates a code of length 26 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+48x^64+159x^68+162x^72+174x^76+3072x^78+150x^80+135x^84+105x^88+48x^92+27x^96+12x^100+3x^104

The gray image is a linear code over GF(4) with n=104, k=6 and d=64.
This code was found by Heurico 1.16 in 0.0619 seconds.