The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1 a^6*X  1  1  1  1  1  1  1  1  1  1  1 a^2*X  1  1  1  1  1  1  1  1  1  1  1  1 a^5*X  1  1  1  1  1  1  1 a^6*X a*X  1  1  1  1  1  1  1
 0  1  0  1  a a^2 a^6*X+a^3 a^6*X+a^4 a^5 a^6 a^6*X a^6*X+1 X+a X+a^2  1 a^6*X+a^5  X a^5*X+1 a^5*X+a^3 a^6*X+a^2 a^4 a*X+a^3 a^5*X+a^5 a^6*X+a^6 a^4*X+a a^5*X+a^6  1 a^4 a^5*X+a^4 a^5*X a^2*X+1 a^3*X+a^6 a^6*X+a a^3 a^2*X+a^2 X+a^4 a^2*X+a^6 a*X+a^5 a^3*X+a^3  1 a^2*X a^3*X+a^2 X+a^6 a^2*X+a^5 a^6*X+a^4 a^2  0  1  1  1 a^3*X+1 a^3*X+a^4 a^3*X+a^2 X+a^5  X a^5*X
 0  0  1 a^6  a a^4  1 a^5 a^3 a^2 a^3*X+1 a*X+a^5 a^6*X a^5*X+a^2 X+a^6 X+1 a^5*X+a^3 a^6*X+a a^5*X+a^6 a^5*X a^5*X+a^4 X+a a^2*X+a^2 a^2*X+a^5 a^6*X+a^4 a^4*X+a^3 a^4*X+a a^6*X+a^6 a^5*X+1 a^5*X+a^5 a^5*X+a^4 a^2*X+a a*X+a^6 a^3*X+a^2 a*X+a^3 a^3*X+a X+a^6 a^6*X+a^4 a^4*X a^6*X+a^2 a*X+a^4 a^3*X+1  1 a^4*X+a^5 a^3*X+a^2 a^5*X+a a*X+a^2 a*X+a^4 a^4*X+a^3 a^3*X+a^3 a^2*X+a^6 a^3*X a*X+a^2 a^6 a*X+a  0

generates a code of length 56 over F8[X]/(X^2) who´s minimum homogenous weight is 375.

Homogenous weight enumerator: w(x)=1x^0+3584x^375+5180x^376+1904x^377+56x^378+336x^380+5040x^381+5880x^382+20440x^383+21392x^384+2968x^385+784x^386+1120x^388+10080x^389+7056x^390+29904x^391+28294x^392+8512x^393+2744x^394+2128x^396+17136x^397+12152x^398+39256x^399+31577x^400+4536x^401+63x^408+7x^416+7x^432+7x^440

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