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

generates a code of length 56 over GR(16,4) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+66x^144+216x^148+393x^152+432x^156+387x^160+768x^162+381x^164+4608x^166+423x^168+6912x^170+384x^172+378x^176+450x^180+216x^184+180x^188+96x^192+57x^196+21x^200+12x^204+3x^216

The gray image is a code over GF(4) with n=224, k=7 and d=144.
This code was found by Heurico 1.16 in 2.41 seconds.