The generator matrix

 1  0  0  1  1  1  X  1  1
 0  1  0  1 X^2+X X^2+X+1  1  0  0
 0  0  1  1 X^2+X+1 X^2+X  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  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+55x^4+128x^5+176x^6+576x^7+285x^8+1664x^9+264x^10+576x^11+197x^12+128x^13+40x^14+6x^16

The gray image is a linear code over GF(2) with n=36, k=12 and d=8.
This code was found by Heurico 1.16 in 0.00763 seconds.