The generator matrix

 1  0  0  0  0  1  1  1  1 X^2  1 X^2  X  1  0  1 X^2+X  1  1 X^2 X^2  1  1  X  1  1  1  X  1  1  0 X^2+X X^2+X X^2+X X^2+X  1  0  1 X^2  1  1
 0  1  0  0  0  0  X  1 X^2+1  1 X^2+X+1  1  1  0  X X^2+1  1 X+1  X  1  1  X X^2+1  X X^2+1  0 X^2+X+1 X^2+X  X X^2  1  X  1 X^2  1  1  1 X^2  X  0  0
 0  0  1  0  0  0 X+1  X X^2+1 X^2+X+1  X X+1  X  1  1 X^2+1  1  0 X^2+X  1  X X^2 X^2+X+1  0  0 X^2+1 X^2+1  1  1 X^2+X+1  0  1  0 X^2+X X^2 X^2+1 X^2 X^2  1  1  0
 0  0  0  1  0  1  1 X+1 X^2  1  0  0 X+1 X^2+X X^2+X+1  1  0 X^2+X+1 X^2+1  1 X^2+X  0 X+1  1 X+1  X X^2+1 X^2+X X+1 X+1  1  1 X^2+X+1  1 X^2 X^2+X X^2+1 X^2 X^2  0  0
 0  0  0  0  1  1 X^2  0  X  X X+1  1 X^2+X+1 X^2+X+1 X^2+1 X^2+1 X^2 X+1  X X^2+X+1 X^2+X+1  1 X^2+X  1  1 X^2+X  1 X+1 X^2+X X^2+X+1 X^2+X  X  1 X^2+X X+1  X  0  X X^2+X+1  1  0
 0  0  0  0  0  X  0  0  0  0  0 X^2 X^2  0 X^2 X^2+X  X X^2+X X^2+X X^2+X  X  X X^2+X X^2+X X^2 X^2  0  X  X X^2  X X^2 X^2+X X^2+X X^2  X X^2  X  X X^2+X  0

generates a code of length 41 over Z2[X]/(X^3) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+86x^31+347x^32+1016x^33+1656x^34+3320x^35+4753x^36+7922x^37+9512x^38+13876x^39+14447x^40+16930x^41+14239x^42+14268x^43+10007x^44+8008x^45+4595x^46+3150x^47+1423x^48+860x^49+389x^50+180x^51+60x^52+14x^53+9x^54+2x^56+2x^57

The gray image is a linear code over GF(2) with n=164, k=17 and d=62.
This code was found by Heurico 1.13 in 106 seconds.