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  0  4
 0  0  0  0  0  2  4

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

Homogenous weight enumerator: w(x)=1x^0+95x^2+328x^3+1693x^4+4960x^5+14595x^6+22192x^7+14595x^8+4960x^9+1693x^10+328x^11+95x^12+1x^14

The gray image is a code over GF(2) with n=28, k=16 and d=4.
This code was found by Heurico 1.16 in 0.7 seconds.