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

generates a code of length 72 over F8[X]/(X^2) who´s minimum homogenous weight is 472.

Homogenous weight enumerator: w(x)=1x^0+77x^472+616x^480+840x^488+588x^496+3584x^497+483x^504+25088x^505+441x^512+252x^520+217x^528+231x^536+224x^544+56x^552+49x^560+21x^568

The gray image is a linear code over GF(8) with n=576, k=5 and d=472.
This code was found by Heurico 1.16 in 0.789 seconds.