The generator matrix

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

generates a code of length 12 over GR(16,4) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+33x^28+75x^32+822x^36+48x^40+33x^44+12x^48

The gray image is a code over GF(4) with n=48, k=5 and d=28.
This code was found by Heurico 1.16 in -1.01e-007 seconds.