The generator matrix

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

generates a code of length 41 over Z2[X]/(X^3) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+166x^34+476x^35+664x^36+1278x^37+1218x^38+1672x^39+1539x^40+2278x^41+1578x^42+1940x^43+1197x^44+1102x^45+608x^46+384x^47+146x^48+74x^49+44x^50+8x^51+3x^52+4x^53+2x^54+2x^56

The gray image is a linear code over GF(2) with n=164, k=14 and d=68.
This code was found by Heurico 1.13 in 2.12 seconds.