The generator matrix

 1  0  0  0  0  1  1  1 X^2+X  1  0  1  1  1 X^2  X  X X^2+X X^2  1 X^2+X  1  0  0  1  1  0  1  1  0  1  X X^2 X^2 X^2  1 X^2+X X^2+X X^2+X  1  1  X  1
 0  1  0  0  0  0 X^2  0 X^2 X+1  1  1  1 X^2  1  1  1 X^2+X X^2+X X+1  1 X^2  1  1 X^2+X+1  1 X^2+X  0  X  X X^2+X+1  1 X^2+X  0 X^2+X  1  X  1  1  1 X^2  X  0
 0  0  1  0  0  0  1  1  1 X^2+1 X^2+X+1 X^2+X X+1  X X^2+1 X^2+X X^2  X  1 X^2+X+1 X+1 X+1 X^2+1  0  0 X^2+X+1 X^2 X^2  1  1 X^2+X+1  1  X  1  1  0  1  0  X  0 X+1 X^2  0
 0  0  0  1  0  1  1  X X^2+X+1 X^2  1 X^2+X X^2+X+1 X^2+1 X^2  1 X^2+X  1  0  X  X X^2 X+1 X^2+1  1 X+1  1  0 X+1 X^2+X+1 X^2+X+1 X^2+1  1  X  X X^2+X+1 X^2+1 X+1 X^2+X+1 X^2  0  1  0
 0  0  0  0  1  1  X X+1 X+1 X^2+1  X X+1 X^2+X+1 X^2  1 X^2+X+1 X^2+X+1 X^2+1 X+1  X X^2 X^2+X X+1  X  0  0 X^2 X^2+X+1 X^2+1  0 X^2+1 X^2+X  1  0 X^2+X+1 X^2+X+1  0  X X^2 X+1 X+1 X^2+1  0
 0  0  0  0  0 X^2  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  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+127x^34+470x^35+1082x^36+1902x^37+2677x^38+3774x^39+5063x^40+6300x^41+7317x^42+7564x^43+7543x^44+6844x^45+5303x^46+3800x^47+2494x^48+1580x^49+918x^50+438x^51+195x^52+78x^53+40x^54+18x^55+6x^56+2x^58

The gray image is a linear code over GF(2) with n=172, k=16 and d=68.
This code was found by Heurico 1.13 in 29.8 seconds.