The generator matrix

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

generates a code of length 18 over GR(16,4) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+72x^53+144x^54+9x^56+24x^57+6x^60

The gray image is a code over GF(4) with n=72, k=4 and d=53.
This code was found by Heurico 1.16 in 6.87e-008 seconds.