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

generates a code of length 41 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+210x^104+339x^108+465x^112+192x^114+468x^116+1728x^118+447x^120+5184x^122+513x^124+5184x^126+444x^128+438x^132+417x^136+213x^140+90x^144+42x^148+6x^152+3x^156

The gray image is a linear code over GF(4) with n=164, k=7 and d=104.
This code was found by Heurico 1.16 in 1.69 seconds.