The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  1  1  1
 0  1  0  0  1  0  1 a+1 2a+2  a 2a+3 2a  3  0
 0  0  1  0 3a+3  1  1  a  2  a  2 2a+3 2a+2  0
 0  0  0  1  1 3a+3  a  a a+1 a+2  2  0  1  2
 0  0  0  0 2a+2  2 2a  2 2a+2  0 2a 2a+2  0 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+120x^28+108x^29+156x^30+528x^31+1329x^32+1920x^33+1296x^34+2640x^35+7206x^36+13080x^37+6696x^38+14256x^39+28914x^40+38016x^41+12816x^42+30576x^43+40692x^44+37788x^45+9756x^46+7296x^47+5610x^48+1248x^49+78x^52+18x^56

The gray image is a code over GF(4) with n=56, k=9 and d=28.
This code was found by Heurico 1.16 in 28.4 seconds.