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

generates a code of length 52 over GR(64,4) who´s minimum homogenous weight is 336.

Homogenous weight enumerator: w(x)=1x^0+189x^336+112x^338+56x^339+959x^344+1120x^345+3864x^346+3472x^347+2730x^352+5600x^353+14616x^354+8064x^355+10311x^360+21280x^361+44744x^362+23408x^363+17283x^368+29344x^369+51352x^370+22344x^371+371x^376+399x^384+245x^392+238x^400+42x^408

The gray image is a code over GF(8) with n=416, k=6 and d=336.
This code was found by Heurico 1.16 in 12.1 seconds.