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

generates a code of length 76 over F8[X]/(X^2) who´s minimum homogenous weight is 504.

Homogenous weight enumerator: w(x)=1x^0+539x^504+280x^507+784x^510+1232x^511+3598x^512+6440x^515+3136x^518+5040x^519+9835x^520+16632x^523+6048x^526+14224x^527+13181x^528+46648x^531+11200x^534+30352x^535+21595x^536+44688x^539+7504x^542+6496x^543+11816x^544+245x^552+161x^560+196x^568+119x^576+112x^584+28x^592+14x^600

The gray image is a linear code over GF(8) with n=608, k=6 and d=504.
This code was found by Heurico 1.16 in 18 seconds.