The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+123x^28+48x^30+387x^32+384x^33+288x^34+690x^36+1152x^37+432x^38+552x^40+27x^44+12x^48

The gray image is a code over GF(4) with n=48, k=6 and d=28.
This code was found by Heurico 1.16 in 0.0107 seconds.