The generator matrix

 1  0  0  1  1  1  1  1  1  1 2a+2  1 2a+2  1  1  1  1  1  1  1  2
 0  1  0  0  2 2a+2  1 3a+2 3a+3  1  1 a+1  1  a 2a+3 a+1 3a+3 a+2  a 2a+3  1
 0  0  1  1 3a+2 3a+3 3a+3 3a+1 3a+1  3 a+3  2  3 a+2  a  a  3  0  1  2 3a
 0  0  0 2a+2 2a 2a  2  2 2a+2 2a+2  2  0  0 2a  0  2  0 2a  2 2a+2 2a+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+2124x^56+4032x^60+6111x^64+4032x^68+84x^72

The gray image is a code over GF(4) with n=84, k=7 and d=56.
This code was found by Heurico 1.16 in 41.1 seconds.