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

generates a code of length 66 over F8[X]/(X^2) who´s minimum homogenous weight is 432.

Homogenous weight enumerator: w(x)=1x^0+140x^432+707x^440+777x^448+1344x^449+567x^456+8064x^457+532x^464+19264x^465+392x^472+280x^480+245x^488+224x^496+147x^504+70x^512+14x^520

The gray image is a linear code over GF(8) with n=528, k=5 and d=432.
This code was found by Heurico 1.16 in 0.711 seconds.