The generator matrix

 1  0  0  1  1  1  X  1  1 X^2+X  1 X^2  1  1 X^2+X  1  1 X^2  1  X  1  1  0  1 X^2+X  X  1  1  1  0  0 X^2+X  X X^2  1  1  1  1  1  1  0
 0  1  0  X  1 X^2+X+1  1 X^2+X  0 X^2  1  1 X^2+X X^2+1  1 X+1  1  X  0  1  X X^2+X+1  1  0  0  1 X^2+X+1  X  1  0  1  1  X  1 X^2+1 X^2+1 X^2 X+1 X^2 X^2+X  1
 0  0  1  1 X^2+X+1 X^2+X  1 X+1 X^2+X  1  1  1  0  0  0 X+1  X  1 X+1  X X^2+X  1 X+1 X^2+X+1  1 X^2+1  0 X^2 X^2+X  1 X^2+X X^2+X+1  1 X^2+X  0 X^2+1 X^2+X+1 X^2+1 X^2+X X^2+X  0
 0  0  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 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+69x^34+200x^35+322x^36+646x^37+591x^38+994x^39+799x^40+1016x^41+874x^42+926x^43+568x^44+592x^45+238x^46+174x^47+95x^48+48x^49+17x^50+10x^51+6x^52+2x^53+3x^54+1x^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 1.68 seconds.