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

generates a code of length 54 over GR(64,4) who´s minimum homogenous weight is 336.

Homogenous weight enumerator: w(x)=1x^0+532x^336+1981x^344+2429x^352+3374x^360+3584x^364+4095x^368+50176x^372+4354x^376+175616x^380+5145x^384+4508x^392+3654x^400+1785x^408+777x^416+126x^424+7x^432

The gray image is a code over GF(8) with n=432, k=6 and d=336.
This code was found by Heurico 1.16 in 33 seconds.