The generator matrix

 1  0  0  0  1  1  1 X^2+X  1
 0  1  0  0  1  X X^2  0  0
 0  0  1  0  1  0 X+1  1  0
 0  0  0  1  1 X+1  0  1  0
 0  0  0  0  X  X X^2+X X^2+X X^2
 0  0  0  0  0 X^2 X^2  0 X^2

generates a code of length 9 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+77x^4+248x^5+1295x^6+2848x^7+7843x^8+8144x^9+7843x^10+2848x^11+1295x^12+248x^13+77x^14+1x^18

The gray image is a linear code over GF(2) with n=36, k=15 and d=8.
This code was found by Heurico 1.16 in 0.509 seconds.