The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  1  X  1  0  1  1 X^2+X  1  1  1  1  1  X  1  1 X^2+X X^2+X  1  1  1  1  1  1  0  X  1 X^2+X  1 X^2  0  1
 0  1  1  0 X^2+X+1  1  X X^2+X+1  1  1 X^2+X  1 X^2  1 X+1  0  1 X^2+1 X^2+X+1 X^2+X X^2+X+1  X  1 X^2+X X+1  1  1  1 X^2  1  0 X^2+X+1 X^2+X  0  X  X  1 X^2  X X^2  0
 0  0  X  0 X^2+X  0  0 X^2 X^2  0  0 X^2  X X^2+X X^2 X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X^2 X^2  X  0 X^2+X  0  0 X^2+X X^2+X  0  X  X  X X^2 X^2+X X^2  0  X  X  0
 0  0  0  X  0  0 X^2+X X^2+X X^2+X  X X^2 X^2+X X^2 X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X  X X^2+X X^2+X X^2 X^2  X  X X^2+X X^2  X X^2+X X^2+X  0 X^2 X^2+X X^2 X^2  X  X  0  0
 0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0  0  0  0 X^2  0  0
 0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0  0  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+37x^34+124x^35+161x^36+348x^37+279x^38+560x^39+340x^40+576x^41+280x^42+474x^43+224x^44+332x^45+140x^46+110x^47+35x^48+24x^49+27x^50+10x^51+7x^52+5x^54+2x^55

The gray image is a linear code over GF(2) with n=164, k=12 and d=68.
This code was found by Heurico 1.16 in 0.479 seconds.