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.