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

generates a code of length 49 over GR(64,4) who´s minimum homogenous weight is 312.

Homogenous weight enumerator: w(x)=1x^0+98x^312+616x^319+483x^320+448x^322+448x^323+2128x^325+6328x^327+812x^328+448x^329+3136x^330+4032x^331+7056x^333+14952x^335+609x^336+6272x^337+3136x^338+19264x^339+22512x^341+34664x^343+644x^344+21952x^345+21952x^346+33600x^347+25648x^349+29456x^351+399x^352+378x^360+371x^368+182x^376+105x^384+14x^392

The gray image is a code over GF(8) with n=392, k=6 and d=312.
This code was found by Heurico 1.16 in 11.2 seconds.