The generator matrix

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

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+21x^38+42x^40+384x^43+42x^46+21x^48+1x^86

The gray image is a linear code over GF(2) with n=172, k=9 and d=76.
This code was found by Heurico 1.16 in 0.0422 seconds.