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.