The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+50x^3+202x^4+664x^5+1845x^6+2668x^7+1845x^8+664x^9+202x^10+50x^11+1x^14

The gray image is a linear code over GF(2) with n=28, k=13 and d=6.
This code was found by Heurico 1.11 in 6.87e-008 seconds.