The generator matrix

 1  0  0  1  1  1 2a+2  1  1  0  1  1
 0  1  0  1  a 3a+3  1  2  3  1 2a+2 2a+3
 0  0  1 3a+3  a  1  1 3a 2a+3 a+2  1  a
 0  0  0  2  0  2 2a+2  0  2 2a 2a 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+414x^28+576x^30+1539x^32+3456x^34+2892x^36+5184x^38+2268x^40+54x^44

The gray image is a code over GF(4) with n=48, k=7 and d=28.
This code was found by Heurico 1.16 in 0.094 seconds.