The generator matrix
1 1 1 1 1 2 1
0 2 0 0 0 4 2
0 0 2 0 2 4 4
0 0 0 2 2 6 6
0 0 0 0 4 0 4
generates a code of length 7 over Z8 who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+77x^4+296x^6+256x^7+331x^8+56x^10+7x^12
The gray image is a code over GF(2) with n=28, k=10 and d=8.
This code was found by Heurico 1.16 in 0.00558 seconds.