The generator matrix

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

generates a code of length 20 over GR(16,4) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+336x^54+783x^56+720x^58+600x^60+432x^62+789x^64+432x^66+3x^72

The gray image is a code over GF(4) with n=80, k=6 and d=54.
This code was found by Heurico 1.16 in 0.031 seconds.