The generator matrix

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

generates a code of length 18 over GR(16,4) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+78x^48+72x^52+768x^54+54x^56+24x^60+9x^64+18x^72

The gray image is a code over GF(4) with n=72, k=5 and d=48.
This code was found by Heurico 1.16 in 3.24e-008 seconds.