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

generates a code of length 68 over F8[X]/(X^2) who´s minimum homogenous weight is 467.

Homogenous weight enumerator: w(x)=1x^0+4704x^467+7840x^468+245x^472+3136x^475+2240x^476+231x^480+6496x^483+7840x^484+28x^488+7x^504

The gray image is a linear code over GF(8) with n=544, k=5 and d=467.
This code was found by Heurico 1.16 in 84.5 seconds.