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

generates a code of length 84 over F8[X]/(X^2) who´s minimum homogenous weight is 560.

Homogenous weight enumerator: w(x)=1x^0+364x^560+56x^561+1176x^564+1232x^567+2429x^568+2464x^569+12936x^572+3752x^575+5005x^576+4200x^577+29400x^580+5992x^583+7168x^584+7000x^585+69720x^588+11256x^591+10878x^592+9856x^593+58800x^596+6440x^599+6034x^600+5096x^601+252x^608+140x^616+140x^624+161x^632+98x^640+84x^648+14x^656

The gray image is a linear code over GF(8) with n=672, k=6 and d=560.
This code was found by Heurico 1.16 in 20.1 seconds.