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

generates a code of length 79 over F8[X]/(X^2) who´s minimum homogenous weight is 520.

Homogenous weight enumerator: w(x)=1x^0+84x^520+56x^525+336x^527+504x^528+1232x^530+2240x^531+2072x^533+1344x^535+798x^536+8288x^538+9744x^539+5544x^541+3808x^543+756x^544+16128x^546+17808x^547+16968x^549+8512x^551+504x^552+34720x^554+33712x^555+26880x^557+14672x^559+378x^560+25648x^562+22512x^563+5824x^565+217x^568+245x^576+231x^584+161x^592+77x^600+84x^608+49x^616+7x^624

The gray image is a linear code over GF(8) with n=632, k=6 and d=520.
This code was found by Heurico 1.16 in 19.9 seconds.