The generator matrix

 1  1  1  1
 0  2  0  2
 0  0  2 2a+2

generates a code of length 4 over GR(16,4) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+18x^8+216x^12+21x^16

The gray image is a code over GF(4) with n=16, k=4 and d=8.
This code was found by Heurico 1.16 in 3.24e-008 seconds.