The generator matrix

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

generates a code of length 7 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+15x^4+36x^5+114x^6+184x^7+109x^8+36x^9+14x^10+3x^12

The gray image is a linear code over GF(2) with n=28, k=9 and d=8.
This code was found by Heurico 1.16 in 0.000447 seconds.