The generator matrix

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

generates a code of length 41 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+90x^108+48x^109+168x^111+300x^112+516x^113+612x^115+561x^116+828x^117+1152x^119+810x^120+1512x^121+1944x^123+1014x^124+1704x^125+1656x^127+837x^128+1236x^129+612x^131+318x^132+300x^133+45x^136+51x^140+36x^144+27x^148+3x^152+3x^156

The gray image is a linear code over GF(4) with n=164, k=7 and d=108.
This code was found by Heurico 1.16 in 0.843 seconds.