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

generates a code of length 78 over F8[X]/(X^2) who´s minimum homogenous weight is 517.

Homogenous weight enumerator: w(x)=1x^0+336x^517+448x^518+525x^520+280x^522+504x^523+1736x^524+3024x^525+2800x^526+784x^528+1736x^530+2408x^531+5600x^532+10920x^533+7616x^534+700x^536+5656x^538+5880x^539+13104x^540+19656x^541+15008x^542+476x^544+11032x^546+11256x^547+21728x^548+32424x^549+19712x^550+455x^552+9968x^554+8624x^555+15176x^556+19656x^557+11760x^558+392x^560+217x^568+147x^576+147x^584+119x^592+77x^600+42x^608+7x^616+7x^624

The gray image is a linear code over GF(8) with n=624, k=6 and d=517.
This code was found by Heurico 1.16 in 19.2 seconds.