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

generates a code of length 52 over GR(64,4) who´s minimum homogenous weight is 336.

Homogenous weight enumerator: w(x)=1x^0+189x^336+686x^344+770x^352+3584x^357+658x^360+25088x^365+539x^368+371x^376+378x^384+252x^392+140x^400+105x^408+7x^416

The gray image is a code over GF(8) with n=416, k=5 and d=336.
This code was found by Heurico 1.16 in 0.53 seconds.