The generator matrix

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

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+93x^4+680x^5+1119x^6+3680x^7+6979x^8+7664x^9+6979x^10+3680x^11+1119x^12+680x^13+93x^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 0.49 seconds.