The generator matrix

 1  0  1  1  1  1  1
 0  1  1  0  0  0  0
 0  0  X  0  X  0  0
 0  0  0  X  X  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+39x^2+32x^3+293x^4+192x^5+2227x^6+2624x^7+2227x^8+192x^9+293x^10+32x^11+39x^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 0.0199 seconds.