The generator matrix

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

generates a code of length 50 over GR(16,4) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+1245x^144+1128x^148+732x^152+468x^156+435x^160+84x^164+3x^176

The gray image is a code over GF(4) with n=200, k=6 and d=144.
This code was found by Heurico 1.16 in 3.13 seconds.