The generator matrix

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

generates a code of length 14 over GR(16,4) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+66x^36+99x^40+768x^42+36x^44+3x^48+42x^52+9x^56

The gray image is a code over GF(4) with n=56, k=5 and d=36.
This code was found by Heurico 1.16 in 0.063 seconds.