The generator matrix

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

generates a code of length 43 over Z2[X]/(X^3) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+138x^35+532x^36+848x^37+1495x^38+1766x^39+2931x^40+2800x^41+4310x^42+3232x^43+4240x^44+2788x^45+2863x^46+1884x^47+1567x^48+696x^49+409x^50+142x^51+68x^52+36x^53+9x^54+6x^55+5x^56+1x^62+1x^66

The gray image is a linear code over GF(2) with n=172, k=15 and d=70.
This code was found by Heurico 1.16 in 25.5 seconds.