The generator matrix
1 1 1 1 1 1 X 1 X 1
0 X 0 0 0 0 X^2+X X^2 X^2 X
0 0 X 0 0 X^2 X X^2+X 0 X^2
0 0 0 X 0 X^2+X X^2 X X X
0 0 0 0 X X X^2+X 0 X^2 X^2
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+40x^6+160x^7+194x^8+256x^9+560x^10+576x^11+184x^12+40x^14+32x^15+5x^16
The gray image is a linear code over GF(2) with n=40, k=11 and d=12.
This code was found by Heurico 1.16 in 0.0105 seconds.