The generator matrix
1 1 1 1 2 1 1
0 12 0 0 0 8 4
0 0 12 0 0 4 8
0 0 0 12 12 12 12
0 0 0 0 8 8 0
generates a code of length 7 over Z16 who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+77x^4+296x^6+1280x^7+331x^8+56x^10+7x^12
The gray image is a code over GF(2) with n=56, k=11 and d=16.
This code was found by Heurico 1.16 in 0.00253 seconds.