The generator matrix

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

generates a code of length 87 over F8[X]/(X^2) who´s minimum homogenous weight is 589.

Homogenous weight enumerator: w(x)=1x^0+4144x^589+2408x^590+112x^591+413x^592+392x^593+1232x^594+5264x^595+5040x^596+18144x^597+8624x^598+1288x^599+3836x^600+1848x^601+3864x^602+11424x^603+7840x^604+27552x^605+13328x^606+2464x^607+4312x^608+2296x^609+4704x^610+10640x^611+8624x^612+29792x^613+13552x^614+3304x^615+6181x^616+2632x^617+4536x^618+12096x^619+7168x^620+24304x^621+8680x^622+28x^624+14x^632+28x^640+14x^648+14x^656+7x^664

The gray image is a linear code over GF(8) with n=696, k=6 and d=589.
This code was found by Heurico 1.16 in 17.9 seconds.