The generator matrix

 1  0  1  1  1 12  1
 0  1  1  0 11  1  8
 0  0  2  6  0  2  4
 0  0  0 12 12 12  8

generates a code of length 7 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+66x^4+304x^5+1725x^6+4000x^7+1725x^8+304x^9+66x^10+1x^14

The gray image is a code over GF(2) with n=56, k=13 and d=16.
This code was found by Heurico 1.16 in 0.0158 seconds.