The generator matrix

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

generates a code of length 51 over GR(16,4) who´s minimum homogenous weight is 143.

Homogenous weight enumerator: w(x)=1x^0+1176x^143+384x^144+2472x^147+1206x^148+2628x^151+792x^152+2652x^155+702x^156+2076x^159+741x^160+972x^163+246x^164+312x^167+12x^168+6x^172+6x^176

The gray image is a code over GF(4) with n=204, k=7 and d=143.
This code was found by Heurico 1.16 in 12.2 seconds.