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

generates a code of length 59 over GR(64,4) who´s minimum homogenous weight is 368.

Homogenous weight enumerator: w(x)=1x^0+343x^368+1463x^376+2450x^384+3101x^392+3815x^400+28672x^406+3962x^408+200704x^414+4900x^416+4424x^424+3997x^432+2499x^440+1253x^448+455x^456+105x^464

The gray image is a code over GF(8) with n=472, k=6 and d=368.
This code was found by Heurico 1.16 in 37.6 seconds.