The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  X  X  0  X  1  1  1  0  1  X  X  X  1  1 X^2  0
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X X^2+X X^2+X  0 X^2+X X^2+X  0  0 X^2+X X^2 X^2  0  X  X X^2 X^2+X  X X^2+X  0  0 X^2+X  0  X  X X^2  X  X
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2  0  X  0 X^2 X^2  0 X^2+X X^2+X X^2  X X^2+X X^2  0 X^2+X  X  0  X  X  X X^2  0  0  X  0 X^2 X^2+X
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2  0 X^2 X^2+X X^2+X X^2+X X^2  X X^2 X^2+X X^2 X^2+X  0 X^2+X  0 X^2 X^2+X  0  X  0 X^2+X X^2+X X^2+X X^2  X X^2+X
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 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+168x^34+12x^35+315x^36+96x^37+468x^38+236x^39+635x^40+320x^41+590x^42+260x^43+437x^44+96x^45+250x^46+4x^47+129x^48+58x^50+15x^52+2x^54+3x^56+1x^60

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 1.44 seconds.