The generator matrix

 1  0  1  1  1  X  1
 0  1  1  0  0  0  0
 0  0  X  0  0  X  0
 0  0  0  X  0  X  0
 0  0  0  0  X  X  0
 0  0  0  0  0 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+53x^2+68x^3+347x^4+752x^5+1647x^6+2456x^7+1647x^8+752x^9+347x^10+68x^11+53x^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 0.0234 seconds.