The generator matrix

 1  0  0  1  1  1 X^2+X  1  1
 0  1  0  1  0  1  1  0  0
 0  0  1  1  1  0  1  0  0
 0  0  0  X  0  0  X X^2+X X^2+X
 0  0  0  0  X  0  X X^2+X  X
 0  0  0  0  0  X  X X^2 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+145x^4+96x^5+1410x^6+2816x^7+7665x^8+8512x^9+7644x^10+2816x^11+1431x^12+96x^13+130x^14+6x^16

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 0.596 seconds.