The generator matrix

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

generates a code of length 41 over F4[X]/(X^2) who´s minimum homogenous weight is 116.

Homogenous weight enumerator: w(x)=1x^0+285x^116+360x^117+192x^118+408x^119+345x^120+420x^121+192x^122+312x^123+222x^124+168x^125+108x^126+120x^127+90x^128+324x^129+24x^130+72x^131+270x^132+72x^133+60x^134+48x^135+3x^140

The gray image is a linear code over GF(4) with n=164, k=6 and d=116.
This code was found by Heurico 1.16 in 14.5 seconds.