The generator matrix

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

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+94x^34+230x^35+380x^36+516x^37+712x^38+812x^39+875x^40+1000x^41+918x^42+836x^43+634x^44+484x^45+358x^46+156x^47+81x^48+48x^49+28x^50+14x^51+10x^52+2x^54+3x^56

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 1.91 seconds.