The generator matrix

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

generates a code of length 53 over GR(16,4) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+465x^144+732x^145+408x^146+2328x^148+1896x^149+1440x^150+3900x^152+3768x^153+1896x^154+5373x^156+5376x^157+2796x^158+6762x^160+6012x^161+3048x^162+5931x^164+4536x^165+2136x^166+3066x^168+2064x^169+504x^170+717x^172+192x^173+60x^174+51x^176+33x^180+18x^184+18x^188+9x^192

The gray image is a code over GF(4) with n=212, k=8 and d=144.
This code was found by Heurico 1.16 in 94.1 seconds.