The generator matrix

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

generates a code of length 70 over F8[X]/(X^2) who´s minimum homogenous weight is 474.

Homogenous weight enumerator: w(x)=1x^0+6888x^474+12040x^475+4312x^476+336x^478+63x^480+27944x^482+28392x^483+9632x^484+1120x^486+224x^488+34552x^490+36120x^491+8120x^492+2128x^494+217x^496+41720x^498+38136x^499+10192x^500+7x^528

The gray image is a linear code over GF(8) with n=560, k=6 and d=474.
This code was found by Heurico 1.16 in 13.8 seconds.