The generator matrix

 1  0  0  0  1  1  1
 0  1  0  0  3  0  0
 0  0  1  0  1  0  0
 0  0  0  1  1  0  0
 0  0  0  0  4  0  0
 0  0  0  0  0  4  0
 0  0  0  0  0  0  4

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

Homogenous weight enumerator: w(x)=1x^0+79x^2+192x^3+909x^4+1920x^5+7715x^6+11136x^7+7715x^8+1920x^9+909x^10+192x^11+79x^12+1x^14

The gray image is a code over GF(2) with n=28, k=15 and d=4.
This code was found by Heurico 1.16 in 0.201 seconds.