The generator matrix

 1  0  0  0  0  1  1
 0  1  0  0  0  1  0
 0  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^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+125x^2+540x^3+2531x^4+6480x^5+13215x^6+19752x^7+13215x^8+6480x^9+2531x^10+540x^11+125x^12+1x^14

The gray image is a linear code over GF(2) with n=28, k=16 and d=4.
This code was found by Heurico 1.13 in -6.48e-008 seconds.