The generator matrix

 1  0  0  1  1  1  0
 0  1  0  1  2  7  1
 0  0  1  1  1  0  3
 0  0  0  2  0  6  4
 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+125x^4+384x^5+888x^6+1280x^7+923x^8+384x^9+104x^10+7x^12

The gray image is a code over GF(2) with n=28, k=12 and d=8.
This code was found by Heurico 1.16 in 0.00919 seconds.