The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1 X^2+X  1  1  1  1  X  1 X^2+X  1 X^2  0  1  1  1  1  1 X^2+X  1  1  1  1  0  1 X^2+X  0  1  X  1  0
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1  X  1 X^2+1  1  0 X^2 X^2+1 X^2+1  1  X  1 X^2+X+1  1  1 X^2+X X^2 X^2+X X^2+X X^2+X  1  1 X^2+X X^2  1  1  0  1  1 X+1  1 X^2+X  1
 0  0  X  0 X^2+X  0 X^2+X X^2 X^2+X X^2+X  X X^2 X^2  0  X  0  X X^2+X  X X^2+X  X X^2+X  0 X^2  X  0 X^2 X^2+X X^2 X^2+X  0 X^2+X  0  0 X^2 X^2  0  0  0  X  0
 0  0  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2
 0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0  0  0  0 X^2  0
 0  0  0  0  0  0 X^2  0  0 X^2  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  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+38x^34+84x^35+190x^36+162x^37+487x^38+340x^39+593x^40+378x^41+570x^42+340x^43+454x^44+150x^45+165x^46+60x^47+29x^48+14x^49+16x^50+8x^51+12x^52+3x^54+1x^56+1x^62

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 0.486 seconds.