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

generates a code of length 56 over F8[X]/(X^2) who´s minimum homogenous weight is 368.

Homogenous weight enumerator: w(x)=1x^0+602x^368+686x^376+742x^384+29232x^392+434x^400+364x^408+301x^416+196x^424+154x^432+42x^440+14x^448

The gray image is a linear code over GF(8) with n=448, k=5 and d=368.
This code was found by Heurico 1.16 in 0.867 seconds.