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

generates a code of length 55 over GR(64,4) who´s minimum homogenous weight is 344.

Homogenous weight enumerator: w(x)=1x^0+798x^344+1855x^352+2737x^360+448x^364+3577x^368+9408x^372+4011x^376+65856x^380+4746x^384+153664x^388+4669x^392+4368x^400+3374x^408+1876x^416+644x^424+105x^432+7x^440

The gray image is a code over GF(8) with n=440, k=6 and d=344.
This code was found by Heurico 1.16 in 34.4 seconds.