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

generates a code of length 41 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+321x^112+48x^114+432x^118+297x^120+1296x^122+1296x^126+189x^128+126x^136+81x^144+9x^152

The gray image is a linear code over GF(4) with n=164, k=6 and d=112.
This code was found by Heurico 1.16 in 3.62 seconds.