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

generates a code of length 42 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+72x^112+204x^116+354x^120+1317x^124+1830x^128+72x^132+93x^136+57x^140+48x^144+18x^148+15x^152+12x^156+3x^160

The gray image is a linear code over GF(4) with n=168, k=6 and d=112.
This code was found by Heurico 1.16 in 0.119 seconds.