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  0  0  X  1  0  0  X X^2  1  1  X X^2  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  X X^2+X  X X^2 X^2  X  0 X^2  X X^2+X X^2  X X^2+X  0  X  X  0  X  X X^2  X X^2+X  0 X^2  0  0  0 X^2 X^2+X X^2+X X^2  X
 0  0  X  0  0  0  X X^2+X  X  X  X  0  0  X X^2  X X^2  X X^2+X X^2 X^2+X  0 X^2 X^2  0 X^2  0  X  X X^2  0  X  X X^2 X^2+X  X  X  X X^2+X  0  0
 0  0  0  X  0  X  X  X X^2  0  0 X^2 X^2 X^2 X^2+X X^2+X X^2 X^2+X X^2+X X^2+X  X  X  X  0  X  X  X X^2+X X^2  0  0 X^2  X X^2+X X^2+X X^2 X^2+X X^2  0  X  X
 0  0  0  0  X  X X^2 X^2+X X^2+X  0  X  X  0 X^2+X  X X^2  X  X X^2 X^2+X  0  0  0 X^2+X X^2+X X^2  0  X X^2 X^2+X X^2  0 X^2+X  0 X^2+X X^2+X X^2+X X^2+X X^2+X  X X^2
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2  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+156x^34+12x^35+273x^36+144x^37+358x^38+476x^39+276x^40+768x^41+302x^42+516x^43+262x^44+112x^45+198x^46+20x^47+138x^48+70x^50+9x^52+4x^54+1x^64

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 0.769 seconds.