The generator matrix

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

generates a code of length 19 over GR(16,4) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+144x^53+360x^54+36x^56+96x^57+24x^60+144x^61+216x^62+3x^64

The gray image is a code over GF(4) with n=76, k=5 and d=53.
This code was found by Heurico 1.16 in -1.01e-007 seconds.