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

generates a code of length 57 over GR(64,4) who´s minimum homogenous weight is 368.

Homogenous weight enumerator: w(x)=1x^0+91x^368+553x^376+847x^384+644x^392+28672x^399+504x^400+350x^408+434x^416+266x^424+245x^432+77x^440+70x^448+14x^456

The gray image is a code over GF(8) with n=456, k=5 and d=368.
This code was found by Heurico 1.16 in 0.59 seconds.