The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  X  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 a^2*X  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1 a^2*X  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  a a^6*X+a^2 a^6*X+a^4  1  0 a^3 a^6*X+a^6 a^6*X+1 a^5 a^6*X+a^6  a  1 a^6*X+a^4  0 a^6*X+a^2 a^5 X+a^3 a^5*X+a^2 a^6*X+1  X a^3  1 X+a^3  X X+a a^5*X+a^4 a^5*X+a^2 a*X X+a^5 a^2*X+a^3 X+a a^5*X+a^6 a*X+a^5 a^6*X+1  X a^5*X a^5*X+a^6 a^4*X+a a^2*X+a^6 a^3*X+a^6 a^5*X+a^2 a^3*X+a^3 a*X a^5*X+a^4 a*X+a^3 X+a^5  1 a*X+a^3 X+a^3 X+a^5 a*X a^6*X  1 X+a^4 a^3*X+a^3 a^5*X+a^2 X+a^3 a^2*X+a  1 a^5*X+a X+a^2  0 a^4*X+1 a^4*X+a^5 a*X+1 a^5*X+a^4 a^3*X+a^3 X+1 a^4*X+1 a^3*X+a^5 a^4*X+a^6  1 a^3*X+a^6 X+a^6 a^4*X+a^2 a^2*X+a^6 a^3*X+a^4 a^4 a^2*X+a^3  0
 0  0 a^6*X  0  X  X a^3*X  X a^2*X a^3*X a^6*X a^2*X  X a^4*X a^5*X  0 a^6*X  X a^5*X a*X a*X a^4*X a^3*X  X a^5*X a^6*X a^5*X a^5*X a^4*X  X a^4*X a^4*X a^5*X a^4*X a*X a^2*X a*X a^4*X a^6*X  0 a^2*X a^4*X  0  X a^3*X a*X a^2*X  0 a^4*X  0 a^3*X  0 a*X a^5*X a*X a^5*X a^5*X a^2*X  0  0 a^5*X a^5*X a^5*X a^6*X a^3*X  X a^2*X a^5*X a^2*X a*X a^2*X  0 a^6*X a^3*X a^2*X a^3*X  0 a*X a^6*X a^6*X a^3*X a*X a^3*X  0 a^4*X a^3*X  X  X  0
 0  0  0  X a^6*X a^5*X a^3*X a^2*X a^5*X a^6*X a^6*X a^6*X a^5*X a^3*X a^3*X a^2*X a^2*X a*X a^2*X  X  0 a^4*X a*X  X a*X a^4*X a^6*X  X  0 a*X a^6*X  X a^4*X a^3*X a^4*X  X a*X a^5*X a^3*X a^6*X a^4*X a^6*X a^4*X a^5*X a^5*X a*X a^5*X a*X a^5*X a^2*X  0 a^6*X a^2*X  0 a^4*X a^3*X a^6*X  0 a*X a^3*X a^5*X  X a^4*X  X a*X a^6*X  0 a^6*X a^6*X a^5*X a^4*X  0 a^5*X a^4*X a*X a^6*X  X a^5*X a^2*X  0 a^2*X  0 a^5*X  0 a*X  0  X a^4*X a^4*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+140x^592+168x^596+280x^597+504x^599+2023x^600+1232x^602+2072x^604+2912x^605+6832x^607+8820x^608+3640x^610+4648x^612+4424x^613+14112x^615+16961x^616+6328x^618+6888x^620+7224x^621+35280x^623+35224x^624+10920x^626+9744x^628+9408x^629+29288x^631+25970x^632+6552x^634+5152x^636+4424x^637+280x^640+196x^648+112x^656+105x^664+112x^672+91x^680+56x^688+14x^696+7x^704

The gray image is a linear code over GF(8) with n=712, k=6 and d=592.
This code was found by Heurico 1.16 in 22.9 seconds.