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

generates a code of length 56 over GR(64,4) who´s minimum homogenous weight is 368.

Homogenous weight enumerator: w(x)=1x^0+602x^368+686x^376+742x^384+29232x^392+434x^400+364x^408+301x^416+196x^424+154x^432+42x^440+14x^448

The gray image is a code over GF(8) with n=448, k=5 and d=368.
This code was found by Heurico 1.16 in 0.87 seconds.