The generator matrix

 1  0  0  0  1  X  1
 0  1  0  0  1  0  0
 0  0  1  0  1  0  0
 0  0  0  1  1  0  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+93x^2+340x^3+1411x^4+3440x^5+6687x^6+8824x^7+6687x^8+3440x^9+1411x^10+340x^11+93x^12+1x^14

The gray image is a linear code over GF(2) with n=28, k=15 and d=4.
This code was found by Heurico 1.16 in 0.223 seconds.