The generator matrix

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

generates a code of length 41 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+876x^110+1092x^111+294x^112+3312x^114+2784x^115+591x^116+6468x^118+4644x^119+822x^120+9168x^122+6576x^123+984x^124+10116x^126+6108x^127+993x^128+5952x^130+2736x^131+342x^132+972x^134+636x^135+66x^136+3x^148

The gray image is a linear code over GF(4) with n=164, k=8 and d=110.
This code was found by Heurico 1.16 in 61.1 seconds.