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

generates a code of length 56 over GR(64,4) who´s minimum homogenous weight is 375.

Homogenous weight enumerator: w(x)=1x^0+2184x^375+6279x^376+2688x^377+56x^378+168x^379+1288x^380+2800x^381+9072x^382+13496x^383+19880x^384+9128x^385+784x^386+1008x^387+4592x^388+5600x^389+11424x^390+19768x^391+31647x^392+9968x^393+2744x^394+2408x^395+8456x^396+9520x^397+18928x^398+25480x^399+32221x^400+10472x^401+35x^408+28x^416+7x^424+7x^432+7x^448

The gray image is a code over GF(8) with n=448, k=6 and d=375.
This code was found by Heurico 1.16 in 10.8 seconds.