The generator matrix

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

generates a code of length 21 over GR(16,4) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+276x^51+225x^52+204x^53+1104x^54+1524x^55+1593x^56+1224x^57+2868x^58+3864x^59+3828x^60+3408x^61+6324x^62+7368x^63+7200x^64+4824x^65+6588x^66+6132x^67+3489x^68+1092x^69+1548x^70+804x^71+27x^72+18x^76+3x^80

The gray image is a code over GF(4) with n=84, k=8 and d=51.
This code was found by Heurico 1.16 in 4.3 seconds.