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

generates a code of length 55 over GR(64,4) who´s minimum homogenous weight is 360.

Homogenous weight enumerator: w(x)=1x^0+406x^360+854x^368+735x^376+511x^384+28672x^385+406x^392+441x^400+329x^408+210x^416+126x^424+63x^432+14x^440

The gray image is a code over GF(8) with n=440, k=5 and d=360.
This code was found by Heurico 1.16 in 0.562 seconds.