The generator matrix

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

generates a code of length 14 over GR(16,4) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+168x^28+387x^32+1284x^36+5358x^40+8064x^44+756x^48+276x^52+90x^56

The gray image is a code over GF(4) with n=56, k=7 and d=28.
This code was found by Heurico 1.16 in 0.292 seconds.