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

generates a code of length 77 over GR(16,4) who´s minimum homogenous weight is 224.

Homogenous weight enumerator: w(x)=1x^0+60x^224+48x^225+66x^228+288x^229+42x^232+432x^233+45x^236+33x^240+6x^244+3x^300

The gray image is a code over GF(4) with n=308, k=5 and d=224.
This code was found by Heurico 1.16 in 0.078 seconds.