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

generates a code of length 80 over F8[X]/(X^2) who´s minimum homogenous weight is 528.

Homogenous weight enumerator: w(x)=1x^0+126x^528+630x^536+749x^544+588x^552+29190x^560+420x^568+308x^576+189x^584+224x^592+147x^600+119x^608+35x^616+28x^624+7x^632+7x^640

The gray image is a linear code over GF(8) with n=640, k=5 and d=528.
This code was found by Heurico 1.16 in 0.923 seconds.