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

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+840x^110+1068x^111+222x^112+3564x^114+2868x^115+675x^116+5868x^118+4740x^119+954x^120+9756x^122+6096x^123+804x^124+9972x^126+6492x^127+981x^128+5832x^130+2748x^131+390x^132+1032x^134+564x^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 97.9 seconds.