The generator matrix
1 0 0 0 1 1 1 1 X^2 1
0 1 0 0 1 X^2+X X+1 X^2+X 0 0
0 0 1 0 1 0 X+1 X^2+X+1 1 0
0 0 0 1 1 1 X+1 0 X+1 0
0 0 0 0 X X^2+X X^2 X X 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+52x^5+169x^6+620x^7+1988x^8+2888x^9+4895x^10+2968x^11+2004x^12+580x^13+151x^14+60x^15+7x^16+1x^18
The gray image is a linear code over GF(2) with n=40, k=14 and d=10.
This code was found by Heurico 1.13 in 0.078 seconds.