The generator matrix

 1  0  1  1  1  1  1
 0  1  1  0  6  2  0
 0  0  2  6  0  2  4
 0  0  0  4  4  4  0

generates a code of length 7 over Z8 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+15x^4+36x^5+114x^6+184x^7+109x^8+36x^9+14x^10+3x^12

The gray image is a code over GF(2) with n=28, k=9 and d=8.
This code was found by Heurico 1.16 in 0.000385 seconds.