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  1  1  1  1  1  1  1  1  1  1  1  1  0  X  X  1  X  X  1
 0  X  0  0  0  0  0  0  0  0 X^2  X  X X^2+X  0 X^2+X X^2+X  0  X  X X^2+X X^2+X  X  X X^2+X X^2  X X^2 X^2+X X^2  X X^2+X  0 X^2  X  X  X  X X^2 X^2+X X^2+X  0 X^2+X
 0  0  X  0  0  0  0  0  0  0 X^2+X X^2  X  X  X  X  0  X  0 X^2+X X^2+X X^2  X X^2  X X^2 X^2  X X^2+X  X  X  X X^2+X  0 X^2 X^2  0  X X^2+X X^2+X  X X^2  X
 0  0  0  X  0  0  0  X X^2+X  X  X X^2+X  0  X X^2  0 X^2+X X^2+X X^2+X X^2 X^2+X X^2 X^2  X  X  X X^2 X^2 X^2 X^2+X X^2 X^2+X X^2+X  X  0 X^2 X^2+X X^2+X X^2+X X^2+X  0  X X^2+X
 0  0  0  0  X  0  X  X  X X^2  X  X  X X^2 X^2 X^2+X X^2+X X^2 X^2  0 X^2+X X^2+X  0 X^2  0  0  0  X  0  0  X  X  X  X  0 X^2+X  X X^2  0  0 X^2  X X^2+X
 0  0  0  0  0  X  X X^2 X^2+X X^2+X  X  X X^2+X  0  X X^2 X^2 X^2 X^2+X X^2 X^2+X  0 X^2+X  0  X X^2+X  0  0 X^2 X^2+X  X X^2 X^2  X  X X^2 X^2  X X^2 X^2  X  X  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0

generates a code of length 43 over Z2[X]/(X^3) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+298x^34+539x^36+1005x^38+128x^39+1226x^40+1024x^41+3111x^42+1792x^43+2901x^44+1024x^45+1558x^46+128x^47+781x^48+604x^50+175x^52+77x^54+8x^56+3x^58+1x^76

The gray image is a linear code over GF(2) with n=172, k=14 and d=68.
This code was found by Heurico 1.16 in 50.7 seconds.