The generator matrix

 1  1
 0  6

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

Homogenous weight enumerator: w(x)=1x^0+12x^1+102x^2+12x^3+1x^4

The gray image is a code over GF(2) with n=16, k=7 and d=4.
This code was found by Heurico 1.16 in 0.0235 seconds.