The generator matrix

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

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+882x^116+1122x^120+672x^124+1002x^128+399x^132+6x^140+3x^144+9x^148

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 32.5 seconds.