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

generates a code of length 81 over F8[X]/(X^2) who´s minimum homogenous weight is 560.

Homogenous weight enumerator: w(x)=1x^0+2212x^560+112x^568+1771x^576

The gray image is a linear code over GF(8) with n=648, k=4 and d=560.
This code was found by Heurico 1.16 in 17.5 seconds.