The generator matrix

 1  0  0  1  1  1  1
 0  1  0  1  X  0  1
 0  0  1  1 X+1 X+1  0
 0  0  0 X^2  0 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+34x^4+76x^5+272x^6+236x^7+309x^8+68x^9+24x^10+4x^11

The gray image is a linear code over GF(2) with n=28, k=10 and d=8.
This code was found by Heurico 1.11 in 3.81e-009 seconds.