The generator matrix
1 0 0 1 1 1 2
0 1 0 2 5 7 1
0 0 1 1 3 2 1
0 0 0 8 0 0 8
0 0 0 0 8 0 8
0 0 0 0 0 8 8
generates a code of length 7 over Z16 who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+77x^4+2016x^5+5544x^6+17472x^7+5579x^8+2016x^9+56x^10+7x^12
The gray image is a code over GF(2) with n=56, k=15 and d=16.
This code was found by Heurico 1.16 in 0.152 seconds.