The generator matrix

 1  1  1  1  2  8  8
 0  2  0  2 10  2  4
 0  0  2  2  6  4  2

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

Homogenous weight enumerator: w(x)=1x^0+108x^5+138x^6+552x^7+103x^8+108x^9+14x^10

The gray image is a code over GF(2) with n=56, k=10 and d=20.
This code was found by Heurico 1.16 in 0.00142 seconds.