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 aX  1  1 (a+1)X  0  1  1  1  1  1  1  1  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+a aX+a+1 (a+1)X (a+1)X+a+1  0  a X+a+1  1 X+a+1 X+1  X  1 (a+1)X+a aX (a+1)X+a+1 aX  1 aX+1  a (a+1)X+a+1
 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 aX+1 (a+1)X+1 (a+1)X+a+1 (a+1)X+1 aX+1 X+1  a aX+1 X+a+1 aX  1 (a+1)X aX+a (a+1)X a+1 X+a+1 aX+a+1  0 aX+1 X+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)X aX+1 a+1  a aX+1 X+a (a+1)X+1 X+1 X+a  1 (a+1)X+1 X+1  0 aX+a X+1 (a+1)X aX+1  X (a+1)X+1 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+924x^110+996x^111+234x^112+3288x^114+3120x^115+651x^116+6156x^118+4392x^119+882x^120+9648x^122+6528x^123+1008x^124+10068x^126+5844x^127+861x^128+5688x^130+3312x^131+354x^132+1092x^134+384x^135+102x^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 64.3 seconds.