The generator matrix
1 0 1 1 1 0 1 1 1 1
0 1 1 0 X+1 1 0 X X^2+X X
0 0 X 0 0 X X X^2+X 0 X^2
0 0 0 X 0 X X 0 X^2 X^2+X
0 0 0 0 X^2 0 X^2 0 0 X^2
0 0 0 0 0 X^2 0 X^2 X^2 0
generates a code of length 10 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+113x^6+64x^7+488x^8+704x^9+1343x^10+704x^11+524x^12+64x^13+79x^14+11x^16+1x^18
The gray image is a linear code over GF(2) with n=40, k=12 and d=12.
This code was found by Heurico 1.16 in 0.137 seconds.