The generator matrix

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

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+107x^4+296x^5+1756x^6+4744x^7+14004x^8+25680x^9+37896x^10+25680x^11+14004x^12+4744x^13+1756x^14+296x^15+107x^16+1x^20

The gray image is a linear code over GF(2) with n=40, k=17 and d=8.
This code was found by Heurico 1.13 in 0.531 seconds.