The generator matrix

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

generates a code of length 89 over F8[X]/(X^2) who´s minimum homogenous weight is 609.

Homogenous weight enumerator: w(x)=1x^0+1008x^609+504x^610+1512x^611+4704x^615+252x^616+4200x^617+1400x^618+2408x^619+1344x^623+119x^624+2016x^625+616x^626+1400x^627+4704x^631+35x^632+3528x^633+1064x^634+1848x^635+84x^640+21x^648

The gray image is a linear code over GF(8) with n=712, k=5 and d=609.
This code was found by Heurico 1.16 in 65 seconds.