The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  0  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1
 0  1  1  a 3a^2+2 2a^2+3a+1 a^2+3a a^2+3a+3 3a^2+2a+3  a 3a^2+2  0 2a^2+3 a^2+3a+3 a^2+3a 3a^2+2a+3 2a^2+3a+1  1 2a^2+3 a^2+3a+3 2a^2+3a+1  a 3a^2+2 a+2 a^2+3a+1 a^2+3a 3a^2+2a+3 2a^2+3 2a^2+3a+3  1  1  0 3a^2+3 a^2+a 2a^2+a+1 a^2+3a+1 3a^2+2a+2  2 a+2  2 a^2+2a+2 2a^2+3a+3 2a^2 2a^2+2a+3  3 3a^2+2a+2 2a^2+3a+3 2a^2 2a^2+2a+3  1 a^2+3  2  0
 0  0 2a^2+2  0  2  2 2a+2  2 2a^2 2a+2 2a^2+2 2a^2 2a^2  0  0 2a^2 2a^2+2  2  2 2a 2a+2 2a^2+2a 2a+2 2a^2+2  0 2a^2+2a+2 2a^2+2a 2a^2+2a 2a+2 2a^2 2a^2 2a^2  2 2a^2+2 2a^2+2a 2a^2 2a^2 2a+2 2a^2+2a 2a  2 2a 2a 2a^2+2 2a^2+2a  0 2a^2+2a 2a+2 2a^2 2a^2 2a^2+2a  2  0
 0  0  0  2 2a^2+2 2a^2+2a+2 2a+2 2a^2 2a^2+2a+2 2a^2+2 2a^2+2 2a^2+2a 2a 2a^2 2a^2+2a+2  0 2a^2+2a 2a^2+2a+2 2a 2a+2  0 2a^2+2a  2 2a+2 2a 2a^2+2a+2 2a^2+2 2a+2 2a^2  0 2a^2+2 2a^2+2 2a^2 2a^2+2a  2 2a^2+2  2 2a+2 2a+2  0 2a^2+2a+2  2 2a^2+2a+2 2a^2  0 2a^2+2a 2a^2+2a 2a^2+2a 2a^2+2a+2 2a+2 2a^2+2a+2  0 2a+2

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

Homogenous weight enumerator: w(x)=1x^0+224x^344+112x^346+504x^348+224x^351+3024x^352+1064x^353+3304x^354+2408x^356+2016x^359+12068x^360+3528x^361+8232x^362+5880x^364+9632x^367+42966x^368+11256x^369+23352x^370+11256x^372+16800x^375+59234x^376+12824x^377+22344x^378+8624x^380+455x^384+357x^392+210x^400+168x^408+56x^416+21x^424

The gray image is a code over GF(8) with n=424, k=6 and d=344.
This code was found by Heurico 1.16 in 12.3 seconds.