The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+108x^48+96x^49+96x^51+312x^52+576x^53+864x^55+813x^56+1536x^57+2592x^59+1479x^60+2496x^61+2592x^63+1125x^64+1440x^65+150x^68+81x^72+27x^76

The gray image is a code over GF(4) with n=80, k=7 and d=48.
This code was found by Heurico 1.16 in 0.318 seconds.