The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+102x^52+396x^53+204x^56+732x^57+384x^60+1188x^61+279x^64+756x^65+30x^68+12x^72+12x^76

The gray image is a code over GF(4) with n=80, k=6 and d=52.
This code was found by Heurico 1.16 in 0.0228 seconds.