The generator matrix

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

generates a code of length 21 over GR(16,4) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+396x^52+1584x^56+4050x^60+6369x^64+3744x^68+156x^72+66x^76+18x^80

The gray image is a code over GF(4) with n=84, k=7 and d=52.
This code was found by Heurico 1.16 in 59.1 seconds.