The generator matrix

 1  0  0  0  1  1  1
 0  1  0  0  2  5  0
 0  0  1  0  3  1  0
 0  0  0  1  1  2  0
 0  0  0  0  8  0  8

generates a code of length 7 over Z16 who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+130x^3+1002x^4+5528x^5+24085x^6+69580x^7+24085x^8+5528x^9+1002x^10+130x^11+1x^14

The gray image is a code over GF(2) with n=56, k=17 and d=12.
This code was found by Heurico 1.16 in 3.33 seconds.