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

generates a code of length 28 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+135x^72+174x^76+171x^80+768x^81+135x^84+2304x^85+141x^88+105x^92+84x^96+57x^100+12x^104+9x^108

The gray image is a linear code over GF(4) with n=112, k=6 and d=72.
This code was found by Heurico 1.16 in 0.0696 seconds.