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

generates a code of length 70 over F8[X]/(X^2) who´s minimum homogenous weight is 440.

Homogenous weight enumerator: w(x)=1x^0+147x^440+924x^448+2296x^456+2744x^464+3360x^472+3584x^476+3654x^480+50176x^484+3955x^488+175616x^492+3969x^496+4263x^504+3395x^512+2268x^520+1148x^528+490x^536+126x^544+21x^552+7x^560

The gray image is a linear code over GF(8) with n=560, k=6 and d=440.
This code was found by Heurico 1.16 in 45.3 seconds.