The generator matrix

 1  0  0  1  1  1  2
 0  1  0  2  5  7  1
 0  0  1  1  3  2  1

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

Homogenous weight enumerator: w(x)=1x^0+252x^5+714x^6+2184x^7+679x^8+252x^9+14x^10

The gray image is a code over GF(2) with n=56, k=12 and d=20.
This code was found by Heurico 1.16 in -1.53e-008 seconds.