The generator matrix

 1  0  1  1  1 12  2
 0  1  1 12 11  1  2
 0  0  2  6  4  6  2

generates a code of length 7 over Z16 who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+156x^5+330x^6+1096x^7+295x^8+156x^9+14x^10

The gray image is a code over GF(2) with n=56, k=11 and d=20.
This code was found by Heurico 1.16 in 2.1e-008 seconds.