The generator matrix

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

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+44x^35+154x^36+204x^37+302x^38+460x^39+729x^40+800x^41+844x^42+1048x^43+1006x^44+880x^45+568x^46+448x^47+367x^48+144x^49+52x^50+44x^51+38x^52+20x^53+26x^54+4x^55+7x^56+2x^60

The gray image is a linear code over GF(2) with n=172, k=13 and d=70.
This code was found by Heurico 1.16 in 2.32 seconds.