The generator matrix

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

generates a code of length 10 over Z2[X]/(X^3) who�s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+7x^8+48x^10+7x^12+1x^20

The gray image is a linear code over GF(2) with n=40, k=6 and d=16.
This code was found by Heurico 1.16 in 0.000316 seconds.