The generator matrix

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

generates a code of length 20 over GR(16,4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+360x^56+1920x^57+288x^60+375x^64+1152x^65

The gray image is a code over GF(4) with n=80, k=6 and d=56.
This code was found by Heurico 1.16 in 0.079 seconds.