The generator matrix

 1  0  1  1  1  0  X  1  1
 0  1  1  0  1  1  0 X+1 X^2
 0  0  X  0  0  0  X X^2  0
 0  0  0  X  0 X^2+X  0 X^2+X X^2
 0  0  0  0  X  0  X X^2+X X^2+X
 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+32x^4+76x^5+342x^6+848x^7+1672x^8+2248x^9+1676x^10+848x^11+340x^12+76x^13+30x^14+3x^16

The gray image is a linear code over GF(2) with n=36, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0586 seconds.