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

generates a code of length 69 over F8[X]/(X^2) who´s minimum homogenous weight is 432.

Homogenous weight enumerator: w(x)=1x^0+182x^432+896x^440+2030x^448+2765x^456+2891x^464+3801x^472+4039x^480+229376x^483+4151x^488+3773x^496+3612x^504+2597x^512+1344x^520+560x^528+105x^536+7x^544+14x^552

The gray image is a linear code over GF(8) with n=552, k=6 and d=432.
This code was found by Heurico 1.16 in 44.6 seconds.