The generator matrix

 1  0  0  1  1  1  1
 0  1  0  1  X X+1  0
 0  0  1  X  1 X+1  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+22x^4+60x^5+76x^6+204x^7+65x^8+52x^9+28x^10+4x^11

The gray image is a linear code over GF(2) with n=28, k=9 and d=8.
This code was found by Heurico 1.11 in 3.62e-008 seconds.