The generator matrix

 1  0  0  0  1  1  1  X  1 a^2*X  1  1  1  1  1  1  1  1  X  1  1  1  1 a^2*X  1 a*X  1  1  1  1  1  1  1  1 a^2*X  1  1  1 a*X  1 a*X
 0  1  0  0  X  1 X+1  1 a*X  1 a^2*X+a X+a^2 a^2 a*X+1 a*X+a a^2*X+1 a^2  1  1 a*X+a^2 a*X+a^2 a^2 X+1  1  a a*X a*X a*X+a^2 a^2*X  a X+a^2 a*X+a X+a X+a^2  1 a^2*X+1  a X+a  1  1  1
 0  0  1  0 a^2*X+1  1 a^2*X a^2*X+1 X+1 a^2*X+a a^2*X+a^2  X a^2*X+a^2 X+a a*X X+a^2 a^2*X+a X+1  a  1 a*X+a^2 a*X+a^2  X a^2*X  a  1 a*X+1 a^2 a*X a*X+a^2 a^2*X+a a^2*X+a^2 a^2*X+1 a^2*X  a a^2*X+1  0  1 X+a^2 a^2*X+a^2 X+a^2
 0  0  0  1 a^2  X a*X+a^2 a*X+a^2  a a^2*X X+a a^2*X+a^2 a^2*X+1 a*X+1  1 a^2*X X+1 a*X+a^2 a^2*X+a^2  0  X a*X+a^2 a^2*X+a a^2*X+1  a a*X+a^2  1 a*X+a a*X+1 X+a^2 a^2*X  0  1 a^2*X+a  1 X+1 a^2*X+a^2 X+a  X a^2*X+a^2 a^2*X+1

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

Homogenous weight enumerator: w(x)=1x^0+804x^110+1176x^111+231x^112+3408x^114+2820x^115+609x^116+6300x^118+4608x^119+891x^120+9444x^122+6336x^123+1008x^124+10128x^126+6000x^127+984x^128+5724x^130+3132x^131+300x^132+1056x^134+504x^135+69x^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 10.6 seconds.