The generator matrix

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

generates a code of length 41 over F4[X]/(X^2) who´s minimum homogenous weight is 106.

Homogenous weight enumerator: w(x)=1x^0+420x^106+564x^107+792x^108+816x^109+2136x^110+3240x^111+2910x^112+2952x^113+6696x^114+7548x^115+6780x^116+6864x^117+13260x^118+13668x^119+13029x^120+12432x^121+20100x^122+19932x^123+17736x^124+14544x^125+22272x^126+18336x^127+13407x^128+9384x^129+12528x^130+8916x^131+4149x^132+2160x^133+2460x^134+1524x^135+486x^136+42x^140+33x^144+21x^148+3x^152+3x^160

The gray image is a linear code over GF(4) with n=164, k=9 and d=106.
This code was found by Heurico 1.16 in 140 seconds.