The generator matrix

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

generates a code of length 10 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+93x^4+576x^5+512x^6+2624x^7+2210x^8+7040x^9+6656x^10+7040x^11+2210x^12+2624x^13+512x^14+576x^15+93x^16+1x^20

The gray image is a linear code over GF(2) with n=40, k=15 and d=8.
This code was found by Heurico 1.16 in 0.479 seconds.