The generator matrix

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

generates a code of length 9 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+20x^6+64x^7+110x^8+128x^9+104x^10+64x^11+16x^12+4x^14+1x^16

The gray image is a linear code over GF(2) with n=36, k=9 and d=12.
This code was found by Heurico 1.16 in 0.00116 seconds.