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

generates a code of length 89 over F8[X]/(X^2) who´s minimum homogenous weight is 603.

Homogenous weight enumerator: w(x)=1x^0+3640x^603+2128x^604+616x^606+504x^607+3381x^608+4536x^609+5992x^610+17640x^611+8008x^612+2016x^614+3080x^615+10269x^616+10528x^617+8512x^618+25872x^619+11424x^620+3528x^622+3080x^623+10311x^624+10136x^625+9352x^626+25928x^627+8680x^628+4592x^630+4088x^631+12278x^632+10640x^633+8400x^634+23688x^635+9184x^636+70x^640+21x^648+21x^656

The gray image is a linear code over GF(8) with n=712, k=6 and d=603.
This code was found by Heurico 1.16 in 19.2 seconds.