The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+414x^224+396x^226+1152x^227+660x^228+180x^230+222x^232+132x^236+138x^240+180x^242+384x^243+216x^244+12x^246+6x^248+3x^256

The gray image is a code over GF(4) with n=308, k=6 and d=224.
This code was found by Heurico 1.16 in 50.8 seconds.