The generator matrix

 1  0  1  1  1  4  2
 0  1  1  0  3  1 14
 0  0  2  0  2  4  2
 0  0  0  2  2  6  6

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

Homogenous weight enumerator: w(x)=1x^0+178x^4+656x^5+3917x^6+6880x^7+3917x^8+656x^9+178x^10+1x^14

The gray image is a code over GF(2) with n=56, k=14 and d=16.
This code was found by Heurico 1.16 in 0.0611 seconds.