The generator matrix

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

generates a code of length 20 over GR(16,4) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+264x^52+1536x^53+900x^56+3072x^57+1584x^60+4608x^61+1263x^64+3072x^65+72x^68+12x^72

The gray image is a code over GF(4) with n=80, k=7 and d=52.
This code was found by Heurico 1.16 in 17.2 seconds.