The generator matrix

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

generates a code of length 51 over GR(16,4) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+243x^144+348x^146+726x^148+348x^150+585x^152+324x^154+462x^156+372x^158+276x^160+144x^162+222x^164+30x^168+6x^172+6x^176+3x^184

The gray image is a code over GF(4) with n=204, k=6 and d=144.
This code was found by Heurico 1.16 in 0.0819 seconds.