The generator matrix

 1  0  0  0  1  1  1
 0  1  0  0  1  2  3
 0  0  1  0  1  3  2
 0  0  0  1  2  1  3

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

Homogenous weight enumerator: w(x)=1x^0+154x^4+224x^5+1253x^6+832x^7+1253x^8+224x^9+154x^10+1x^14

The gray image is a code over GF(2) with n=28, k=12 and d=8.
This code was found by Heurico 1.11 in 0.0733 seconds.