The generator matrix

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

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+52x^39+153x^40+154x^41+200x^42+120x^43+86x^44+44x^45+67x^46+44x^47+42x^48+14x^49+20x^50+16x^51+6x^52+4x^53+1x^54

The gray image is a linear code over GF(2) with n=172, k=10 and d=78.
This code was found by Heurico 1.11 in 0.031 seconds.