The generator matrix

 1  0  1  6  2
 0  1  6  1  6
 0  0  8  8  0

generates a code of length 5 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+162x^4+192x^5+152x^6+5x^8

The gray image is a code over GF(2) with n=40, k=9 and d=16.
This code was found by Heurico 1.16 in 0.00118 seconds.