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

generates a code of length 81 over F8[X]/(X^2) who´s minimum homogenous weight is 536.

Homogenous weight enumerator: w(x)=1x^0+168x^536+686x^544+777x^552+4214x^560+25578x^568+357x^576+203x^584+210x^592+182x^600+154x^608+126x^616+84x^624+14x^632+14x^640

The gray image is a linear code over GF(8) with n=648, k=5 and d=536.
This code was found by Heurico 1.16 in 0.942 seconds.