The generator matrix

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

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+22x^6+32x^7+170x^8+64x^9+168x^10+32x^11+20x^12+2x^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 0.000842 seconds.