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

generates a code of length 77 over F8[X]/(X^2) who´s minimum homogenous weight is 512.

Homogenous weight enumerator: w(x)=1x^0+385x^512+819x^520+728x^528+3584x^532+581x^536+25088x^540+385x^544+364x^552+175x^560+280x^568+91x^576+161x^584+77x^592+35x^600+14x^608

The gray image is a linear code over GF(8) with n=616, k=5 and d=512.
This code was found by Heurico 1.16 in 0.875 seconds.