The generator matrix

 1  0  0  0  1  1  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  2  4  0

generates a code of length 7 over Z8 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+76x^2+202x^3+614x^4+1080x^5+3405x^6+5628x^7+3405x^8+1080x^9+614x^10+202x^11+76x^12+1x^14

The gray image is a code over GF(2) with n=28, k=14 and d=4.
This code was found by Heurico 1.11 in -6.29e-008 seconds.