The generator matrix

 1  1
 0 12

generates a code of length 2 over Z16 who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+4x^1+54x^2+4x^3+1x^4

The gray image is a code over GF(2) with n=16, k=6 and d=4.
This code was found by Heurico 1.16 in 0.0223 seconds.