The generator matrix

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

generates a code of length 6 over GR(16,4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+45x^16+192x^18+18x^24

The gray image is a code over GF(4) with n=24, k=4 and d=16.
This code was found by Heurico 1.16 in -6.87e-008 seconds.