The generator matrix

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

generates a code of length 81 over F8[X]/(X^2) who´s minimum homogenous weight is 561.

Homogenous weight enumerator: w(x)=1x^0+616x^561+392x^566+1344x^567+35x^568+1568x^569+56x^574+56x^577+21x^584+7x^592

The gray image is a linear code over GF(8) with n=648, k=4 and d=561.
This code was found by Heurico 1.16 in 5.84 seconds.