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

generates a code of length 51 over GR(64,4) who´s minimum homogenous weight is 312.

Homogenous weight enumerator: w(x)=1x^0+238x^312+1232x^320+2156x^328+3535x^336+13167x^344+70322x^352+159012x^360+4851x^368+3941x^376+2499x^384+994x^392+168x^400+28x^408

The gray image is a code over GF(8) with n=408, k=6 and d=312.
This code was found by Heurico 1.16 in 31.4 seconds.