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  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  0  0 a*X  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  0 a^3*X a^5*X  X  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^3*X  X a^5*X  0  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  X  X a*X a^5*X

generates a code of length 82 over F8[X]/(X^2) who´s minimum homogenous weight is 544.

Homogenous weight enumerator: w(x)=1x^0+168x^544+742x^552+742x^560+3584x^567+728x^568+25088x^575+420x^576+378x^584+203x^592+175x^600+210x^608+112x^616+105x^624+91x^632+7x^640+14x^648

The gray image is a linear code over GF(8) with n=656, k=5 and d=544.
This code was found by Heurico 1.16 in 0.957 seconds.