The generator matrix

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

generates a code of length 76 over F8[X]/(X^2) who´s minimum homogenous weight is 512.

Homogenous weight enumerator: w(x)=1x^0+2765x^512+728x^514+840x^515+2296x^516+2240x^517+5992x^518+5040x^519+12488x^520+504x^521+5152x^522+6552x^523+8232x^524+7280x^525+9632x^526+8568x^527+18277x^528+1232x^529+11704x^530+9464x^531+12488x^532+6944x^533+12040x^534+7168x^535+17969x^536+1848x^537+14672x^538+11816x^539+12824x^540+8624x^541+11760x^542+7896x^543+16982x^544+56x^552+63x^560+7x^568

The gray image is a linear code over GF(8) with n=608, k=6 and d=512.
This code was found by Heurico 1.16 in 16.4 seconds.