The generator matrix

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

generates a code of length 10 over Z2[X]/(X^3) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+36x^5+97x^6+152x^7+356x^8+828x^9+1135x^10+848x^11+372x^12+156x^13+79x^14+24x^15+7x^16+4x^17+1x^18

The gray image is a linear code over GF(2) with n=40, k=12 and d=10.
This code was found by Heurico 1.16 in 0.37 seconds.