The generator matrix

 1  0  1  1  1  2
 0  1 2a+3  2 2a+1  1

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

Homogenous weight enumerator: w(x)=1x^0+81x^16+96x^18+72x^20+6x^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 -3.24e-008 seconds.