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

generates a code of length 40 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+201x^108+123x^112+192x^114+237x^116+1152x^118+45x^120+1728x^122+153x^124+51x^128+114x^132+24x^136+51x^140+9x^144+9x^148+3x^152+3x^156

The gray image is a linear code over GF(4) with n=160, k=6 and d=108.
This code was found by Heurico 1.16 in 0.557 seconds.