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

generates a code of length 76 over F8[X]/(X^2) who´s minimum homogenous weight is 504.

Homogenous weight enumerator: w(x)=1x^0+308x^504+868x^512+602x^520+609x^528+28672x^532+476x^536+322x^544+245x^552+245x^560+189x^568+98x^576+77x^584+42x^592+7x^600+7x^608

The gray image is a linear code over GF(8) with n=608, k=5 and d=504.
This code was found by Heurico 1.16 in 0.861 seconds.