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^2  0  0  0
 0  0  0  0 X^2  0  0
 0  0  0  0  0 X^2  0
 0  0  0  0  0  0 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+43x^2+48x^3+201x^4+480x^5+1547x^6+3552x^7+1547x^8+480x^9+201x^10+48x^11+43x^12+1x^14

The gray image is a linear code over GF(2) with n=28, k=13 and d=4.
This code was found by Heurico 1.16 in 0.0155 seconds.