The generator matrix

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

generates a code of length 51 over GR(16,4) who´s minimum homogenous weight is 139.

Homogenous weight enumerator: w(x)=1x^0+120x^139+225x^140+1056x^143+525x^144+1764x^147+729x^148+2688x^151+756x^152+3552x^155+900x^156+2496x^159+672x^160+612x^163+132x^164+45x^168+48x^172+21x^176+21x^180+9x^184+9x^188+3x^192

The gray image is a code over GF(4) with n=204, k=7 and d=139.
This code was found by Heurico 1.16 in 1.63 seconds.