The generator matrix

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

generates a code of length 52 over GR(64,4) who´s minimum homogenous weight is 347.

Homogenous weight enumerator: w(x)=1x^0+2856x^347+7112x^348+112x^350+336x^351+2212x^352+2240x^353+5488x^354+16240x^355+22232x^356+448x^357+1568x^358+2016x^359+6867x^360+4480x^361+7840x^362+24808x^363+41720x^364+3136x^365+5488x^366+4816x^367+12817x^368+7616x^369+11760x^370+31360x^371+36456x^372+28x^376+42x^384+14x^392+14x^400+7x^408+14x^416

The gray image is a code over GF(8) with n=416, k=6 and d=347.
This code was found by Heurico 1.16 in 26.3 seconds.