The generator matrix

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

generates a code of length 7 over Z2[X]/(X^3) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+76x^2+202x^3+614x^4+1080x^5+3405x^6+5628x^7+3405x^8+1080x^9+614x^10+202x^11+76x^12+1x^14

The gray image is a linear code over GF(2) with n=28, k=14 and d=4.
This code was found by Heurico 1.13 in -1.01e-007 seconds.