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

generates a code of length 71 over F8[X]/(X^2) who´s minimum homogenous weight is 472.

Homogenous weight enumerator: w(x)=1x^0+651x^472+721x^480+651x^488+469x^496+28672x^497+483x^504+329x^512+266x^520+224x^528+119x^536+105x^544+63x^552+7x^560+7x^568

The gray image is a linear code over GF(8) with n=568, k=5 and d=472.
This code was found by Heurico 1.16 in 44.5 seconds.