The generator matrix

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

generates a code of length 49 over GR(16,4) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+501x^144+360x^148+54x^152+96x^156+12x^160

The gray image is a code over GF(4) with n=196, k=5 and d=144.
This code was found by Heurico 1.16 in 0.359 seconds.