The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+87x^28+192x^30+585x^32+384x^33+1152x^34+2400x^36+3456x^37+2304x^38+9687x^40+10368x^41+3456x^42+13791x^44+10368x^45+5184x^46+2004x^48+90x^52+27x^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 2.05 seconds.