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

generates a code of length 83 over F8[X]/(X^2) who´s minimum homogenous weight is 552.

Homogenous weight enumerator: w(x)=1x^0+266x^552+791x^560+707x^568+623x^576+28672x^581+385x^584+385x^592+287x^600+203x^608+140x^616+126x^624+91x^632+49x^640+21x^648+14x^656+7x^664

The gray image is a linear code over GF(8) with n=664, k=5 and d=552.
This code was found by Heurico 1.16 in 0.968 seconds.