The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  2  0  2  2 2a+2 2a+2 2a+2 2a+2 2a+2 2a+2  0  0  2  2 2a  0
 0  0  2  0 2a+2  2 2a+2  0 2a+2 2a+2  2  2 2a+2  2  0  2 2a+2  0 2a+2 2a
 0  0  0  2  2  2 2a 2a+2  0  2  0  2 2a 2a 2a 2a+2  0 2a 2a  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+36x^52+87x^56+810x^60+54x^64+12x^68+9x^72+6x^76+9x^80

The gray image is a code over GF(4) with n=80, k=5 and d=52.
This code was found by Heurico 1.16 in 0 seconds.