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

generates a code of length 66 over F8[X]/(X^2) who´s minimum homogenous weight is 416.

Homogenous weight enumerator: w(x)=1x^0+350x^416+1680x^424+2177x^432+3248x^440+7168x^448+54103x^456+179984x^464+4249x^472+3731x^480+2877x^488+1568x^496+791x^504+182x^512+28x^520+7x^528

The gray image is a linear code over GF(8) with n=528, k=6 and d=416.
This code was found by Heurico 1.16 in 42.8 seconds.