The generator matrix

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

generates a code of length 16 over GR(16,4) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+72x^36+156x^40+174x^44+3282x^48+180x^52+168x^56+54x^60+9x^64

The gray image is a code over GF(4) with n=64, k=6 and d=36.
This code was found by Heurico 1.16 in 0.0286 seconds.