The generator matrix

 1  0  0  1  1  1 14
 0  1  0  1 12 13  1
 0  0  1  1  0  3  2
 0  0  0  2  6  4  6

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

Homogenous weight enumerator: w(x)=1x^0+274x^4+1232x^5+6893x^6+15968x^7+6893x^8+1232x^9+274x^10+1x^14

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 5.01 seconds.