The generator matrix
1 1 1 1 1 1 1 1 X X
0 X 0 0 0 0 0 X X^2+X X^2+X
0 0 X 0 0 0 X 0 X X
0 0 0 X 0 X X X 0 0
0 0 0 0 X X 0 0 X X
0 0 0 0 0 X^2 0 0 0 X^2
0 0 0 0 0 0 X^2 0 0 X^2
0 0 0 0 0 0 0 X^2 0 X^2
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+92x^4+560x^6+3046x^8+8992x^10+3036x^12+560x^14+97x^16
The gray image is a linear code over GF(2) with n=40, k=14 and d=8.
This code was found by Heurico 1.16 in 0.242 seconds.