The generator matrix

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

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+44x^4+104x^6+128x^7+398x^8+768x^9+272x^10+128x^11+188x^12+8x^14+9x^16

The gray image is a linear code over GF(2) with n=36, k=11 and d=8.
This code was found by Heurico 1.16 in 0.00402 seconds.