The generator matrix

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

generates a code of length 75 over F8[X]/(X^2) who´s minimum homogenous weight is 504.

Homogenous weight enumerator: w(x)=1x^0+2030x^504+280x^505+280x^507+672x^508+840x^509+2016x^510+7728x^511+15190x^512+952x^513+2128x^514+3864x^515+6832x^516+5040x^517+7392x^518+14616x^519+24465x^520+2352x^521+4704x^522+7560x^523+9408x^524+5320x^525+7392x^526+14784x^527+26369x^528+2072x^529+7504x^530+9800x^531+11760x^532+6720x^533+8288x^534+16632x^535+25515x^536+1512x^537+56x^544+42x^552+28x^560

The gray image is a linear code over GF(8) with n=600, k=6 and d=504.
This code was found by Heurico 1.16 in 16.1 seconds.