The generator matrix
1 0 1 1 1 X^2 1 1 1
0 1 1 0 X+1 1 0 X^2+X X^2
0 0 X 0 X X^2 X X^2+X 0
0 0 0 X X X^2+X X^2+X X^2+X 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+45x^6+108x^7+213x^8+300x^9+206x^10+100x^11+42x^12+4x^13+5x^14
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 0.00274 seconds.