The generator matrix
1 0 1 1 1 X^2+X 1 1 1
0 1 1 X^2+X X+1 1 X^2+X+1 X^2+1 X^2+X+1
0 0 X 0 0 X^2 X^2+X X^2 X
0 0 0 X^2 0 X^2 X^2 0 0
0 0 0 0 X^2 0 0 X^2 X^2
generates a code of length 9 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+44x^6+80x^7+342x^8+96x^9+336x^10+80x^11+40x^12+4x^14+1x^16
The gray image is a linear code over GF(2) with n=36, k=10 and d=12.
This code was found by Heurico 1.16 in 0.00232 seconds.