The generator matrix

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

generates a code of length 43 over Z2[X]/(X^3) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+98x^39+159x^40+128x^41+104x^42+106x^43+123x^44+90x^45+86x^46+60x^47+32x^48+20x^49+1x^50+4x^51+2x^52+2x^53+2x^55+2x^56+1x^58+2x^59+1x^60

The gray image is a linear code over GF(2) with n=172, k=10 and d=78.
This code was found by Heurico 1.16 in 3.55 seconds.