The generator matrix
1 0 0 1 1 1 2
0 1 0 2 1 3 1
0 0 1 1 3 6 1
0 0 0 4 0 0 4
0 0 0 0 4 0 4
0 0 0 0 0 4 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+672x^5+168x^6+2240x^7+203x^8+672x^9+56x^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 0.00859 seconds.