The generator matrix

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

generates a code of length 70 over F8[X]/(X^2) who´s minimum homogenous weight is 462.

Homogenous weight enumerator: w(x)=1x^0+224x^462+406x^464+224x^465+224x^466+3192x^470+1120x^471+875x^472+6608x^473+2016x^474+8176x^478+5600x^479+672x^480+16464x^481+5152x^482+13216x^486+21280x^487+518x^488+46704x^489+11424x^490+21168x^494+29344x^495+539x^496+44688x^497+9856x^498+11368x^502+350x^504+189x^512+182x^520+133x^528+119x^536+84x^544+28x^552

The gray image is a linear code over GF(8) with n=560, k=6 and d=462.
This code was found by Heurico 1.16 in 17 seconds.