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

generates a code of length 85 over F8[X]/(X^2) who´s minimum homogenous weight is 568.

Homogenous weight enumerator: w(x)=1x^0+518x^568+679x^576+714x^584+602x^592+28672x^595+392x^600+343x^608+273x^616+147x^624+147x^632+77x^640+112x^648+63x^656+21x^664+7x^680

The gray image is a linear code over GF(8) with n=680, k=5 and d=568.
This code was found by Heurico 1.16 in 0.989 seconds.