The generator matrix

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

generates a code of length 91 over F8[X]/(X^2) who´s minimum homogenous weight is 617.

Homogenous weight enumerator: w(x)=1x^0+2072x^617+5320x^618+224x^619+280x^620+1064x^621+1512x^622+4256x^623+6776x^624+11256x^625+17248x^626+560x^627+2520x^628+4424x^629+3528x^630+9520x^631+9471x^632+16520x^633+21784x^634+896x^635+3528x^636+5880x^637+4536x^638+8512x^639+10822x^640+16296x^641+23184x^642+1904x^643+4424x^644+6552x^645+4760x^646+9968x^647+9191x^648+14784x^649+18480x^650+28x^656+35x^664+21x^672+7x^680

The gray image is a linear code over GF(8) with n=728, k=6 and d=617.
This code was found by Heurico 1.16 in 19.8 seconds.