The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+150x^52+153x^56+192x^57+201x^60+1152x^61+150x^64+1728x^65+135x^68+135x^72+87x^76+9x^80+3x^84

The gray image is a code over GF(4) with n=84, k=6 and d=52.
This code was found by Heurico 1.16 in 0.0691 seconds.