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

generates a code of length 68 over F8[X]/(X^2) who´s minimum homogenous weight is 432.

Homogenous weight enumerator: w(x)=1x^0+686x^432+1925x^440+2737x^448+4837x^456+19992x^464+80647x^472+138782x^480+3934x^488+3969x^496+2548x^504+1358x^512+511x^520+203x^528+14x^536

The gray image is a linear code over GF(8) with n=544, k=6 and d=432.
This code was found by Heurico 1.16 in 44.4 seconds.