The generator matrix

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

generates a code of length 41 over F4[X]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+315x^108+192x^109+144x^110+408x^111+2034x^112+912x^113+492x^114+1368x^115+4455x^116+1740x^117+984x^118+2244x^119+7380x^120+2928x^121+1752x^122+3552x^123+9612x^124+3336x^125+1728x^126+3312x^127+7548x^128+2592x^129+924x^130+1320x^131+3165x^132+588x^133+120x^134+84x^135+204x^136+51x^140+27x^144+18x^148+6x^152

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 10.9 seconds.