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
 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
 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+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 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 2a^2+2a+2

generates a code of length 54 over GR(64,4) who´s minimum homogenous weight is 352.

Homogenous weight enumerator: w(x)=1x^0+266x^352+889x^360+763x^368+553x^376+28672x^378+385x^384+476x^392+301x^400+245x^408+126x^416+77x^424+14x^432

The gray image is a code over GF(8) with n=432, k=5 and d=352.
This code was found by Heurico 1.16 in 0.552 seconds.