The generator matrix

 1  0  1  1  1  1  1
 0  1 11  0  0  0  0
 0  0 12  0  0  0  8
 0  0  0 12  0  0  8
 0  0  0  0 12  0  8
 0  0  0  0  0 12  8

generates a code of length 7 over Z16 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+71x^2+184x^3+805x^4+1824x^5+9363x^6+41040x^7+9363x^8+1824x^9+805x^10+184x^11+71x^12+1x^14

The gray image is a code over GF(2) with n=56, k=16 and d=8.
This code was found by Heurico 1.16 in 0.309 seconds.