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

generates a code of length 78 over F8[X]/(X^2) who´s minimum homogenous weight is 520.

Homogenous weight enumerator: w(x)=1x^0+532x^520+700x^528+812x^536+3584x^539+504x^544+25088x^547+455x^552+287x^560+182x^568+224x^576+168x^584+105x^592+70x^600+35x^608+21x^616

The gray image is a linear code over GF(8) with n=624, k=5 and d=520.
This code was found by Heurico 1.16 in 0.914 seconds.