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 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 a^2*X a^5*X 1 1 1 1 1 1 1 a^4*X 1 1 1 1 1 1 a^6*X 1 X a^6*X 1 1 1 1 1 a^2*X 1 1 1 1 1 1 1 1 1 a^3*X 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 1 X+a^4 a^2*X a^4*X+a^2 a^2*X+a^5 a^5*X+a^6 a^4*X+a^3 a^2*X+1 a*X+a a^3*X+1 a*X+a^5 a*X a^6*X+a^6 X+a^3 a^2*X+a^4 a^4*X+a^6 a*X+a^2 a^3*X X+a^5 1 X a^4*X+a^4 a^3*X+a^2 a^3*X+a a^5*X+a^3 a a^5*X+1 a^5*X 1 a^2*X+a^2 a^4*X+a^6 a^5*X+a^5 a*X+a^4 X+a^3 a^2*X+a 1 a^6 0 1 a^4*X+a^4 a^4*X+a^3 a^3*X+1 a^3*X+a X+a^5 1 a a*X a^3*X+a^2 X a^5*X+a^5 a^5*X+a^3 a^6 a*X+1 X+a^2 1 a^4*X+a^5 1 a^2*X+a^2 a^2*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^4*X+a^5 a*X+a^4 X+a^2 a^2*X+a^6 a^4*X+a^5 a^2*X+a X+a^4 a^5*X+a^4 a^2*X+1 a^2*X+a^2 a^6*X+a^4 X+a^6 a*X+1 X a^6*X+a^2 0 a^4*X+1 a*X a^5*X a^4*X+a^3 1 a*X+a^4 a^3*X+a a^3*X+a^5 a^5 a*X+a^2 a*X+a^5 a^2*X+1 a^6 a^6 a^4*X+a^6 X+a^5 a*X+1 a*X+a^6 a^2 X+a^2 a*X+a^2 1 a^3*X+a^5 X+a^3 a^4*X+a^6 a^3*X+a^5 a^5 a^6*X a^3*X+a^3 X+a^2 a^2*X X+a^6 a^5*X+a^5 a^6 a^3*X a*X a^2*X+a^2 a^5*X+1 a^5*X+a^6 a^4*X+a a^5*X+1 a^3*X+a^4 a^3*X+a^2 generates a code of length 86 over F8[X]/(X^2) who´s minimum homogenous weight is 582. Homogenous weight enumerator: w(x)=1x^0+3192x^582+3360x^583+441x^584+616x^585+392x^586+2016x^587+2520x^588+5320x^589+16184x^590+11928x^591+1967x^592+3864x^593+3248x^594+4480x^595+4648x^596+7672x^597+25704x^598+18256x^599+3528x^600+6104x^601+3080x^602+5152x^603+5544x^604+8120x^605+27048x^606+19096x^607+5187x^608+7336x^609+4032x^610+6272x^611+5208x^612+7560x^613+21056x^614+11872x^615+35x^616+21x^624+35x^632+21x^640+21x^648+7x^656 The gray image is a linear code over GF(8) with n=688, k=6 and d=582. This code was found by Heurico 1.16 in 17.7 seconds.