The generator matrix

 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  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  X  0  0  X  X a*X a^2*X a^4*X a^5*X a^5*X  X a^5*X a^6*X  0 a*X a^5*X a*X a^5*X  0 a^4*X a*X a*X a^2*X a*X  X a^4*X a^2*X  X a^3*X a^6*X a^4*X  0  0 a^4*X a^2*X a^2*X a^6*X a^2*X a^3*X a^2*X a^5*X a^2*X a^5*X a^6*X a^4*X a*X a^4*X  X a^4*X  X a^5*X a*X  X a^3*X  X  0 a^2*X a^2*X a*X a^5*X a*X a^4*X a^3*X a^4*X a^2*X a^6*X a^6*X a*X a^6*X a*X  X  X a^4*X a^2*X a^2*X  0  X a*X a^5*X  X a^6*X a^6*X a^2*X a^3*X a^4*X a^5*X a^3*X a^3*X  X  0
 0  0  X  0 a^6*X a^5*X a*X a^6*X a^6*X a*X a^6*X a^2*X a*X a^3*X  X a^5*X  X  X a^4*X a^3*X  X a*X a^4*X  0 a^2*X  0  0 a^2*X a^2*X a^6*X  X a^5*X a^4*X a^6*X  X a^2*X  0 a^6*X a^2*X a^5*X  X a^2*X a^6*X a^5*X a^4*X a^5*X a^4*X a*X a^5*X  0 a^6*X a^2*X  X  0 a^3*X a^3*X a*X a^4*X a^4*X a^5*X a^4*X a^4*X  0 a^3*X a^3*X a^6*X a^4*X a^6*X  X a^5*X a^2*X a^2*X a^3*X a*X  X a*X a*X a^4*X a*X  0 a^3*X  0 a^2*X a^3*X  X a^4*X a^4*X a^5*X  0 a^6*X  0
 0  0  0  X  X a^4*X a^4*X  X a^6*X a^4*X a^6*X a^6*X a^3*X a*X a^4*X a*X a^3*X a^5*X a^6*X a^2*X a^4*X  X  0 a^5*X  0 a^5*X a*X a^6*X a^3*X  0 a^3*X a^6*X a^3*X a^4*X a^2*X a*X  0 a^4*X a^2*X  X a^2*X a^3*X  0 a^5*X a^3*X a^5*X a^2*X a^5*X a^3*X a^4*X a^6*X  0 a^2*X a*X a^2*X  X a^3*X a*X a^6*X a^3*X a^4*X a^3*X a^5*X a^5*X a^4*X a*X a^4*X  X a^3*X a^3*X a*X a^5*X a^2*X a^6*X  X a^4*X  0 a^3*X a^6*X a^4*X a^6*X  0 a^6*X a^6*X  0 a^2*X  0  0 a^2*X a^2*X a*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+280x^608+819x^616+721x^624+609x^632+28672x^637+385x^640+371x^648+210x^656+210x^664+133x^672+112x^680+147x^688+42x^696+35x^704+14x^712+7x^728

The gray image is a linear code over GF(8) with n=728, k=5 and d=608.
This code was found by Heurico 1.16 in 1.09 seconds.