The generator matrix

 1  0  1  1
 0  1 2a+3  a

generates a code of length 4 over GR(16,4) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+48x^9+60x^12+144x^13+3x^16

The gray image is a code over GF(4) with n=16, k=4 and d=9.
This code was found by Heurico 1.16 in 3.24e-008 seconds.