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

generates a code of length 85 over F8[X]/(X^2) who´s minimum homogenous weight is 568.

Homogenous weight enumerator: w(x)=1x^0+763x^568+56x^569+504x^571+3808x^575+5775x^576+840x^577+6888x^579+7560x^583+12376x^584+3864x^585+13944x^587+13608x^591+24906x^592+11032x^593+35448x^595+20888x^599+35056x^600+12880x^601+29232x^603+11480x^607+10332x^608+280x^616+161x^624+182x^632+105x^640+98x^648+49x^656+21x^664+7x^672

The gray image is a linear code over GF(8) with n=680, k=6 and d=568.
This code was found by Heurico 1.16 in 20.8 seconds.