The generator matrix

 1  1  1  1  1  1  1  1  0
 0  X  0  0  0  0  0  X X^2
 0  0  X  0  0  0  X  0 X^2
 0  0  0  X  0  X  X  X  X
 0  0  0  0  X  X  0  0 X^2
 0  0  0  0  0 X^2  0 X^2 X^2
 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+84x^4+128x^5+240x^6+512x^7+1758x^8+2816x^9+1632x^10+512x^11+324x^12+128x^13+48x^14+9x^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 0.0649 seconds.