The generator matrix

 1  0  0  1
 0  1  0  2
 0  0  1  0
 0  0  0  1

generates a code of length 4 over Z16 who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+56x^1+1180x^2+11144x^3+40774x^4+11144x^5+1180x^6+56x^7+1x^8

The gray image is a code over GF(2) with n=32, k=16 and d=4.
This code was found by Heurico 1.16 in 0.281 seconds.