The generator matrix

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

generates a code of length 20 over GR(16,4) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+540x^51+264x^52+2136x^55+852x^56+4176x^59+1704x^60+4584x^63+1191x^64+852x^67+48x^68+36x^72

The gray image is a code over GF(4) with n=80, k=7 and d=51.
This code was found by Heurico 1.16 in 0.234 seconds.