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

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+50x^34+92x^35+143x^36+256x^37+337x^38+418x^39+639x^40+770x^41+892x^42+1022x^43+947x^44+816x^45+566x^46+418x^47+278x^48+172x^49+149x^50+94x^51+70x^52+32x^53+21x^54+4x^55+2x^56+2x^57+1x^66

The gray image is a linear code over GF(2) with n=172, k=13 and d=68.
This code was found by Heurico 1.16 in 3.02 seconds.