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

generates a code of length 39 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+132x^104+171x^108+183x^112+768x^114+99x^116+2304x^118+135x^120+117x^124+45x^128+57x^132+42x^136+36x^140+3x^144+3x^152

The gray image is a linear code over GF(4) with n=156, k=6 and d=104.
This code was found by Heurico 1.16 in 0.109 seconds.