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

generates a code of length 53 over GR(64,4) who´s minimum homogenous weight is 344.

Homogenous weight enumerator: w(x)=1x^0+217x^344+805x^352+742x^360+637x^368+28672x^371+434x^376+483x^384+280x^392+245x^400+161x^408+77x^416+14x^424

The gray image is a code over GF(8) with n=424, k=5 and d=344.
This code was found by Heurico 1.16 in 0.544 seconds.