The generator matrix
1 0 0 1 1 1 X^2+X 1 1 1
0 1 0 1 0 1 1 0 0 0
0 0 1 1 1 0 1 0 0 0
0 0 0 X 0 0 X X^2+X X^2+X 0
0 0 0 0 X 0 X X^2+X X 0
0 0 0 0 0 X X X^2 X^2 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+96x^4+108x^5+597x^6+1468x^7+3380x^8+6616x^9+8235x^10+6616x^11+3380x^12+1468x^13+603x^14+108x^15+87x^16+5x^18
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 0.587 seconds.