The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  X  1  1  1  1  X  1 X^2  1  X  0  1  X  0  X  1  1  1  1
 0  X  0  X  0  0  X X^2+X  0 X^2  X X^2+X  0 X^2+X X^2 X^2+X X^2 X^2+X  X  X  0 X^2+X X^2 X^2+X  0  0 X^2 X^2+X  0  X X^2+X  0  X  X X^2  0  0 X^2 X^2+X X^2+X X^2
 0  0  X  X  0 X^2+X  X  0 X^2  X  X  0 X^2 X^2+X  X  0 X^2+X  0  X X^2+X X^2  X  X X^2+X  X  0  X X^2 X^2+X X^2+X X^2+X X^2+X  0 X^2+X X^2+X  X X^2+X  0  0 X^2  X
 0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2  0 X^2  0  0  0  0 X^2  0
 0  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0  0  0  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+24x^34+60x^35+106x^36+118x^37+172x^38+214x^39+230x^40+272x^41+231x^42+194x^43+134x^44+96x^45+67x^46+42x^47+31x^48+24x^49+16x^50+2x^51+8x^52+2x^53+2x^56+1x^58+1x^62

The gray image is a linear code over GF(2) with n=164, k=11 and d=68.
This code was found by Heurico 1.16 in 0.199 seconds.