The generator matrix

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

generates a code of length 20 over GR(16,4) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+198x^48+324x^49+900x^50+96x^51+1155x^52+1584x^53+2064x^54+864x^55+4671x^56+4824x^57+5688x^58+2592x^59+9279x^60+7344x^61+6480x^62+2592x^63+7002x^64+4356x^65+3300x^66+105x^68+93x^72+21x^76+3x^80

The gray image is a code over GF(4) with n=80, k=8 and d=48.
This code was found by Heurico 1.16 in 51.3 seconds.