The generator matrix

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

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+77x^34+174x^35+411x^36+512x^37+709x^38+756x^39+1095x^40+786x^41+1149x^42+700x^43+753x^44+446x^45+271x^46+148x^47+104x^48+46x^49+30x^50+14x^51+4x^52+2x^53+4x^54

The gray image is a linear code over GF(2) with n=164, k=13 and d=68.
This code was found by Heurico 1.16 in 1.9 seconds.