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

generates a code of length 79 over F8[X]/(X^2) who´s minimum homogenous weight is 544.

Homogenous weight enumerator: w(x)=1x^0+196x^544+1792x^546+119x^552+448x^554+63x^560+1344x^562+133x^568

The gray image is a linear code over GF(8) with n=632, k=4 and d=544.
This code was found by Heurico 1.16 in 0.0812 seconds.