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

generates a code of length 91 over F8[X]/(X^2) who´s minimum homogenous weight is 624.

Homogenous weight enumerator: w(x)=1x^0+49x^624+672x^625+2912x^626+7840x^629+224x^632+1456x^633+3528x^634+2240x^637+126x^640+448x^641+1680x^642+7840x^645+49x^648+1008x^649+2632x^650+28x^656+35x^664

The gray image is a linear code over GF(8) with n=728, k=5 and d=624.
This code was found by Heurico 1.16 in 0.451 seconds.