The generator matrix

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

generates a code of length 91 over F8[X]/(X^2) who´s minimum homogenous weight is 608.

Homogenous weight enumerator: w(x)=1x^0+322x^608+448x^614+4536x^615+3269x^616+2632x^622+19600x^623+7567x^624+5544x^630+34944x^631+14091x^632+11480x^638+68208x^639+21574x^640+8568x^646+44744x^647+13762x^648+266x^656+147x^664+126x^672+70x^680+70x^688+105x^696+35x^704+21x^712+7x^720+7x^728

The gray image is a linear code over GF(8) with n=728, k=6 and d=608.
This code was found by Heurico 1.16 in 23.1 seconds.