The generator matrix

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

generates a code of length 43 over Z2[X]/(X^3) who�s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+69x^38+32x^39+162x^40+64x^41+164x^42+64x^43+152x^44+64x^45+144x^46+32x^47+67x^48+4x^50+1x^54+2x^62+2x^64

The gray image is a linear code over GF(2) with n=172, k=10 and d=76.
This code was found by Heurico 1.16 in 0.0587 seconds.