The generator matrix

 1  0  1  1  1  6  1
 0  1  3  6  5  1  0
 0  0  8  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+16x^5+126x^6+224x^7+127x^8+16x^9+2x^10

The gray image is a code over GF(2) with n=56, k=9 and d=20.
This code was found by Heurico 1.16 in 0.000339 seconds.