The generator matrix

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

generates a code of length 41 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 116.

Homogenous weight enumerator: w(x)=1x^0+873x^116+1128x^120+720x^124+927x^128+414x^132+24x^136+9x^148

The gray image is a linear code over GF(4) with n=164, k=6 and d=116.
This code was found by Heurico 1.16 in 11.8 seconds.