The generator matrix

 1  0  1  1  1  1  1
 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  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+36x^2+42x^3+142x^4+216x^5+845x^6+1532x^7+845x^8+216x^9+142x^10+42x^11+36x^12+1x^14

The gray image is a linear code over GF(2) with n=28, k=12 and d=4.
This code was found by Heurico 1.16 in 0.00432 seconds.