The generator matrix

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

generates a code of length 55 over GR(16,4) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+189x^144+324x^148+438x^152+48x^153+417x^156+576x^157+420x^160+2592x^161+441x^164+5184x^165+420x^168+3888x^169+381x^172+369x^176+285x^180+180x^184+132x^188+57x^192+30x^196+6x^200+6x^204

The gray image is a code over GF(4) with n=220, k=7 and d=144.
This code was found by Heurico 1.16 in 2.4 seconds.