The generator matrix

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

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+71x^2+184x^3+805x^4+2592x^5+6291x^6+12880x^7+6291x^8+2592x^9+805x^10+184x^11+71x^12+1x^14

The gray image is a linear code over GF(2) with n=28, k=15 and d=4.
This code was found by Heurico 1.16 in 0.248 seconds.