The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+16x^4+8x^5+62x^6+80x^7+67x^8+8x^9+10x^10+4x^12

The gray image is a code over GF(2) with n=28, k=8 and d=8.
This code was found by Heurico 1.16 in 0.000241 seconds.