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

generates a code of length 79 over F8[X]/(X^2) who´s minimum homogenous weight is 528.

Homogenous weight enumerator: w(x)=1x^0+637x^528+735x^536+756x^544+3584x^546+518x^552+25088x^554+357x^560+273x^568+231x^576+238x^584+126x^592+98x^600+70x^608+42x^616+14x^624

The gray image is a linear code over GF(8) with n=632, k=5 and d=528.
This code was found by Heurico 1.16 in 43.8 seconds.