The generator matrix

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

generates a code of length 21 over GR(16,4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+570x^56+960x^60+1557x^64+960x^68+30x^72+18x^80

The gray image is a code over GF(4) with n=84, k=6 and d=56.
This code was found by Heurico 1.16 in 0.0237 seconds.