The generator matrix

 1  0  1  1  1  6  1
 0  1  3  6  5  1  0
 0  0  4  4  0  4  4

generates a code of length 7 over Z8 who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+8x^5+46x^6+16x^7+47x^8+8x^9+2x^10

The gray image is a code over GF(2) with n=28, k=7 and d=10.
This code was found by Heurico 1.16 in 0.000187 seconds.