The generator matrix

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

generates a code of length 41 over F4[X]/(X^2) who´s minimum homogenous weight is 115.

Homogenous weight enumerator: w(x)=1x^0+156x^115+108x^116+120x^117+456x^118+624x^119+117x^120+228x^121+444x^122+384x^123+75x^124+72x^125+204x^126+240x^127+54x^128+132x^129+132x^130+276x^131+87x^132+24x^133+108x^134+48x^135+6x^140

The gray image is a linear code over GF(4) with n=164, k=6 and d=115.
This code was found by Heurico 1.16 in 0.031 seconds.