The generator matrix

 1  0  0  0  1  1  1  1 X^2  1  0  0  1  1  0 X^2  1 X^2+X  1  1 X^2+X  X  1  1 X^2  X X^2  1  1 X^2  1  1  1  X  X  1  1 X^2  1  X  1  1  1
 0  1  0  0  0  1 X^2+1  X  1  1  1 X^2+X X^2 X^2+X+1  1  1 X^2 X^2 X^2+X X^2+X  1  1 X+1 X^2+X+1  0  1  1  X  0  1  1 X+1 X+1 X^2+X  1 X+1  X  1  1  X  1  0  0
 0  0  1  0  0 X^2  1 X^2+1 X^2+X+1 X+1 X^2+X  1 X^2+X+1  0  1  X  0 X^2+X X+1  0 X^2+X X^2+1  1 X^2+X  1  X X^2+1 X^2+X+1  1  1 X^2+1 X^2 X^2+1  1 X^2+X X^2+1  X X^2+X X^2  X X^2+X+1 X^2+X X^2+X
 0  0  0  1  1  0 X^2+1 X^2+X  1 X^2+X X+1  1 X^2+1 X^2+X+1 X^2 X^2+X X^2+X+1  1 X^2+1 X^2+1 X+1 X^2  0  0 X^2+X+1 X^2+X X^2+X+1 X^2+X+1  X  1 X^2+X+1  X X^2+X  X X^2 X+1 X^2+X X+1  X  1 X^2+X X^2 X^2+X
 0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0  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+280x^37+349x^38+750x^39+558x^40+1022x^41+643x^42+1084x^43+672x^44+1032x^45+507x^46+634x^47+267x^48+242x^49+61x^50+56x^51+4x^52+12x^53+8x^54+4x^55+2x^56+4x^57

The gray image is a linear code over GF(2) with n=172, k=13 and d=74.
This code was found by Heurico 1.11 in 21.3 seconds.