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

generates a code of length 23 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+102x^56+153x^60+162x^64+138x^68+3072x^69+135x^72+156x^76+129x^80+30x^84+15x^88+3x^92

The gray image is a linear code over GF(4) with n=92, k=6 and d=56.
This code was found by Heurico 1.16 in 0.0521 seconds.