The generator matrix

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

generates a code of length 64 over F8[X]/(X^2) who´s minimum homogenous weight is 416.

Homogenous weight enumerator: w(x)=1x^0+98x^416+56x^422+112x^423+1484x^424+1232x^425+840x^430+1456x^431+8715x^432+8288x^433+3864x^438+4368x^439+21182x^440+16128x^441+11032x^446+11536x^447+46501x^448+34720x^449+12880x^454+11200x^455+39711x^456+25648x^457+343x^464+266x^472+210x^480+175x^488+84x^496+14x^504

The gray image is a linear code over GF(8) with n=512, k=6 and d=416.
This code was found by Heurico 1.16 in 15.5 seconds.