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

generates a code of length 89 over F8[X]/(X^2) who´s minimum homogenous weight is 592.

Homogenous weight enumerator: w(x)=1x^0+189x^592+707x^600+784x^608+4137x^616+25501x^624+469x^632+252x^640+203x^648+168x^656+126x^664+70x^672+84x^680+28x^688+42x^696+7x^704

The gray image is a linear code over GF(8) with n=712, k=5 and d=592.
This code was found by Heurico 1.16 in 1.07 seconds.