The generator matrix

 1  0  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  0  1  1  1  1  2  1  1  1  1  1  1  1  1  2  1
 0  1  1  a 3a^2+2 2a^2+3a+1  0 a^2+3a a^2+3a+3 3a^2+2a+3  2 2a^2+3  a a+2  2 a+2 2a 3a 2a^2+3 2a^2+2a+3 2a+3 2a^2+3a 2a 2a+3 2a+2 2a^2+2a+3 3a 3a^2+2 3a^2+2a+3 2a^2+3a+1  1 2a^2+3a 2a+2 a^2+3a+3 a^2+3a  1 3a^2+3 2a^2+3a+3 3a^2+2a+2 a^2+3a+1  1 3a^2+3 a^2+a 3a^2+2a+2 2a^2+3a+3 a^2+2a+2 a^2+a 3a^2+2a+1 a^2+3a+1  1 3a^2+2a
 0  0 2a^2+2 2a  2  0 2a^2 2a+2 2a^2+2a+2 2a^2+2a 2a^2+2 2a 2a^2+2a 2a^2  2 2a^2+2a+2 2a+2  0 2a+2  2 2a^2+2a 2a^2+2 2a^2+2a+2  0 2a^2+2a 2a^2  2 2a 2a+2 2a 2a^2+2a+2 2a+2 2a 2a^2  0 2a^2+2a 2a^2+2 2a^2+2a+2 2a^2+2a  0  2 2a^2 2a^2+2a+2 2a+2 2a^2+2a 2a^2 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 344.

Homogenous weight enumerator: w(x)=1x^0+70x^344+1344x^345+560x^346+840x^347+4704x^349+217x^352+4480x^353+1120x^354+1008x^355+1344x^357+98x^360+8512x^361+1904x^362+1736x^363+4704x^365+56x^368+56x^376+14x^384

The gray image is a code over GF(8) with n=408, k=5 and d=344.
This code was found by Heurico 1.16 in 0.168 seconds.