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

generates a code of length 57 over GR(64,4) who´s minimum homogenous weight is 368.

Homogenous weight enumerator: w(x)=1x^0+91x^368+56x^371+168x^374+224x^375+1092x^376+56x^378+784x^379+2128x^381+4984x^382+2072x^383+3437x^384+1176x^386+3136x^387+7056x^389+12264x^390+4984x^391+5838x^392+8232x^394+5488x^395+22512x^397+35112x^398+11592x^399+12369x^400+19208x^402+19208x^403+25648x^405+33488x^406+9800x^407+8925x^408+315x^416+322x^424+196x^432+105x^440+63x^448+14x^456

The gray image is a code over GF(8) with n=456, k=6 and d=368.
This code was found by Heurico 1.16 in 13.4 seconds.