The generator matrix

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

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+213x^108+384x^109+96x^110+564x^111+1599x^112+1404x^113+312x^114+1476x^115+3261x^116+3180x^117+444x^118+2916x^119+5310x^120+5184x^121+864x^122+4680x^123+6987x^124+6024x^125+744x^126+3996x^127+5832x^128+4140x^129+456x^130+1620x^131+2085x^132+1164x^133+156x^134+108x^135+210x^136+24x^137+63x^140+18x^144+12x^148+6x^152+3x^156

The gray image is a linear code over GF(4) with n=164, k=8 and d=108.
This code was found by Heurico 1.16 in 11.3 seconds.