The generator matrix

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

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+48x^30+387x^32+384x^33+576x^34+2052x^36+3456x^37+2592x^38+9966x^40+10368x^41+5184x^42+14976x^44+10368x^45+3888x^46+756x^48+276x^52+90x^56

The gray image is a code over GF(4) with n=56, k=8 and d=28.
This code was found by Heurico 1.16 in 2.17 seconds.