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

generates a code of length 98 over F8[X]/(X^2) who´s minimum homogenous weight is 673.

Homogenous weight enumerator: w(x)=1x^0+1232x^673+5208x^674+273x^680+2240x^681+9072x^682+147x^688+1680x^689+3864x^690+21x^696+2016x^697+6944x^698+70x^712

The gray image is a linear code over GF(8) with n=784, k=5 and d=673.
This code was found by Heurico 1.16 in 80.3 seconds.