The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  X  1  1  1  1  1  1  X  1  1 a*X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 a^2*X  1  1 a^2*X  1  1  1  1  1 a*X  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  1  a a^6*X+a^2 a^3 a^6*X+a^4 a^5 a^6*X+a^6  0 a^6*X+1  a a^6*X+a^2 a^6*X+a^4 a^6*X+a^6 a^3 a^5  1  X a^5*X+a^6 X+a X+a^5  1 a^6*X+1 a^5*X+a^2 X+a^3 a^5*X+a^4  X a^5*X+1  1 X+a X+a^3  1 a^5*X+a^2 a^5*X+a^4 X+a^5 a^5*X+1 a*X a^3*X+a^4 a^5*X+a a*X+a^3 a^5*X+a^6 a^4*X+a^2  1 a^4*X+a^4 a*X+a^5 a^3*X+a^6 a*X+a^3 a^3*X+a a^4*X+a^4 X+a^6  1 a^5*X+a a^3*X+a^3  1 a^3*X+1 X+a^6 a^3*X+a^6 a^3*X+a a^3*X+a^3  1 a^3*X+a^4 a^3*X+1 a^5*X+1 a^6*X+1 a*X+1  a X+a a^2*X+a a*X a^6*X a^5*X a^5*X a^6*X  0
 0  0 a^6*X a*X  X  0 a^3*X a^5*X a^4*X a^2*X a*X a^4*X a^3*X  X a^6*X a^5*X a^2*X a*X a^6*X a*X a^5*X  0 a^6*X a^3*X a^4*X  X a^2*X a^5*X a^2*X a^4*X a^6*X a^4*X a^3*X a^5*X a*X a^6*X  X a^3*X a^4*X  0 a^2*X  X a*X a^5*X  0  X a^3*X a^3*X a^2*X a^6*X a^5*X a^5*X a^3*X a*X  X  0 a^2*X  0  X a^6*X a^2*X a^5*X a^4*X a^3*X  X a^6*X a^5*X  0 a^6*X  0 a^3*X a^6*X a^5*X a^2*X  0

generates a code of length 75 over F8[X]/(X^2) who´s minimum homogenous weight is 512.

Homogenous weight enumerator: w(x)=1x^0+1596x^512+1120x^514+6272x^517+4718x^520+2240x^522+1792x^525+1330x^528+3808x^530+6272x^533+3542x^536+35x^544+28x^552+14x^560

The gray image is a linear code over GF(8) with n=600, k=5 and d=512.
This code was found by Heurico 1.16 in 0.326 seconds.