The generator matrix

 1  1  1  1  X  X  X  1  1
 0  X  0 X^2+X  X  X  0  0  0
 0  0 X^2  0  0  0 X^2  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+23x^4+32x^6+32x^7+77x^8+192x^9+56x^10+32x^11+53x^12+8x^14+6x^16

The gray image is a linear code over GF(2) with n=36, k=9 and d=8.
This code was found by Heurico 1.16 in 0.00056 seconds.