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

generates a code of length 48 over GR(64,4) who´s minimum homogenous weight is 312.

Homogenous weight enumerator: w(x)=1x^0+525x^312+756x^320+644x^328+3584x^329+518x^336+25088x^337+581x^344+483x^352+266x^360+196x^368+112x^376+14x^384

The gray image is a code over GF(8) with n=384, k=5 and d=312.
This code was found by Heurico 1.16 in 0.488 seconds.