The generator matrix

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

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+312x^116+408x^117+444x^118+342x^120+480x^121+264x^122+345x^124+240x^125+204x^126+177x^128+288x^129+192x^130+228x^132+120x^133+48x^134+3x^140

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 2.7 seconds.