The generator matrix

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

generates a code of length 52 over GR(16,4) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+285x^144+312x^152+3072x^156+210x^160+102x^168+66x^176+42x^184+3x^192+3x^208

The gray image is a code over GF(4) with n=208, k=6 and d=144.
This code was found by Heurico 1.16 in 42.4 seconds.