The generator matrix

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

generates a code of length 85 over F8[X]/(X^2) who´s minimum homogenous weight is 590.

Homogenous weight enumerator: w(x)=1x^0+840x^590+35x^592+336x^593+1344x^595+1400x^598+112x^601+21x^616+7x^632

The gray image is a linear code over GF(8) with n=680, k=4 and d=590.
This code was found by Heurico 1.16 in 9.13 seconds.