The generator matrix

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

generates a code of length 43 over Z2[X]/(X^3) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+214x^37+507x^38+512x^39+861x^40+784x^41+865x^42+848x^43+885x^44+794x^45+699x^46+474x^47+390x^48+156x^49+115x^50+52x^51+19x^52+4x^53+6x^54+2x^55+4x^56

The gray image is a linear code over GF(2) with n=172, k=13 and d=74.
This code was found by Heurico 1.16 in 4.15 seconds.