The generator matrix

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

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+99x^108+24x^110+132x^111+429x^112+240x^114+696x^115+915x^116+480x^118+1080x^119+1566x^120+912x^122+2016x^123+2019x^124+1032x^126+1572x^127+1332x^128+384x^130+648x^131+633x^132+57x^136+66x^140+30x^144+12x^148+9x^152

The gray image is a linear code over GF(4) with n=164, k=7 and d=108.
This code was found by Heurico 1.16 in 0.833 seconds.