The generator matrix

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

generates a code of length 75 over F8[X]/(X^2) who´s minimum homogenous weight is 496.

Homogenous weight enumerator: w(x)=1x^0+266x^496+749x^504+721x^512+3584x^518+679x^520+25088x^526+371x^528+343x^536+252x^544+238x^552+182x^560+154x^568+98x^576+21x^584+21x^592

The gray image is a linear code over GF(8) with n=600, k=5 and d=496.
This code was found by Heurico 1.16 in 0.831 seconds.