The generator matrix

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

generates a code of length 55 over F8[X]/(X^2) who´s minimum homogenous weight is 375.

Homogenous weight enumerator: w(x)=1x^0+6720x^375+1260x^376+8064x^383+1092x^384+13888x^391+1729x^392+7x^432+7x^440

The gray image is a linear code over GF(8) with n=440, k=5 and d=375.
This code was found by Heurico 1.16 in 86.2 seconds.