The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  2  1  1  1  0  1  1  1  0  1  1  2  1  1  1  1  1  1  1  1  1 2a  1  1  1  1  1 2a 2a  1  0  1 2a+2  1  1  1  1
 0  1  1  a 3a+3  0 2a+3 a+1  a  1  0 2a+3  a  1 a+1 a+2  1 2a+3  0 a+1  1  2  a 2a+3  1  3 a+1  1  1 a+3  2 a+2 2a+2 3a 3a+1 2a+1 2a+1  1  0 a+2 a+2 3a+3 2a+1  1  1 2a+1  1  3  1 2a a+2  1  0
 0  0 2a+2  0  0  0  2  2  2  2  2  2 2a+2 2a+2 2a 2a+2 2a+2 2a  2 2a+2  2 2a+2 2a+2  2  2 2a+2 2a  2 2a  2  0  0 2a+2 2a+2 2a+2  2 2a+2 2a  0 2a+2  2  2 2a+2 2a+2  0  0 2a+2  2  0  2  0 2a+2  2
 0  0  0  2  0  2 2a+2  0  2 2a+2  2  0 2a 2a+2  0  0  2  2 2a 2a+2 2a+2  2  2  0  2  0  2  0 2a+2 2a 2a  2 2a+2 2a 2a+2 2a 2a 2a+2 2a  0 2a  0  0  0  2 2a+2  2 2a+2  0  2 2a  2 2a+2
 0  0  0  0 2a+2 2a+2  2 2a+2 2a  0 2a+2  2  2 2a  2  2  2 2a 2a+2  2 2a  0 2a+2 2a  0 2a+2 2a 2a+2  0  2 2a+2 2a  2  0 2a+2 2a 2a 2a+2 2a  0  0  2 2a  0  0  0  0 2a+2 2a  0 2a 2a+2  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+105x^144+84x^145+240x^147+408x^148+480x^149+732x^151+669x^152+924x^153+1140x^155+633x^156+1296x^157+1608x^159+879x^160+1788x^161+1608x^163+747x^164+1296x^165+732x^167+402x^168+276x^169+84x^171+129x^172+36x^176+24x^180+27x^184+24x^188+9x^192+3x^196

The gray image is a code over GF(4) with n=212, k=7 and d=144.
This code was found by Heurico 1.16 in 1.18 seconds.