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

generates a code of length 70 over F8[X]/(X^2) who´s minimum homogenous weight is 464.

Homogenous weight enumerator: w(x)=1x^0+455x^464+798x^472+448x^476+686x^480+6272x^484+595x^488+21952x^492+420x^496+308x^504+315x^512+175x^520+140x^528+112x^536+56x^544+28x^552+7x^560

The gray image is a linear code over GF(8) with n=560, k=5 and d=464.
This code was found by Heurico 1.16 in 0.755 seconds.