The generator matrix

 1  0  1  1  1 X^2+X  1
 0  1 X+1 X^2+X X^2+1  1  0
 0  0 X^2 X^2  0 X^2 X^2

generates a code of length 7 over Z2[X]/(X^3) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+8x^5+46x^6+16x^7+47x^8+8x^9+2x^10

The gray image is a linear code over GF(2) with n=28, k=7 and d=10.
This code was found by Heurico 1.16 in 0.000172 seconds.