The generator matrix

 1  0  1  1  1  0  1
 0  1  3  6  1  1  0
 0  0  4  0  0  4  0
 0  0  0  4  0  4  0
 0  0  0  0  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+18x^4+64x^5+109x^6+128x^7+109x^8+64x^9+18x^10+1x^14

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 0.000416 seconds.