The generator matrix

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

generates a code of length 20 over GR(16,4) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+276x^49+828x^50+960x^51+720x^52+1236x^53+2484x^54+2892x^55+2082x^56+3660x^57+6876x^58+4572x^59+5526x^60+7068x^61+10044x^62+5220x^63+3402x^64+3120x^65+2808x^66+1716x^67+12x^68+24x^72+6x^76+3x^80

The gray image is a code over GF(4) with n=80, k=8 and d=49.
This code was found by Heurico 1.16 in 4.03 seconds.