The generator matrix

 1  0  1  1  1 14  1
 0  1 11 14  5  1  8
 0  0 12  4  8 12  4

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

Homogenous weight enumerator: w(x)=1x^0+34x^5+258x^6+446x^7+247x^8+30x^9+6x^10+2x^11

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 -5.15e-008 seconds.