The generator matrix

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

generates a code of length 67 over F8[X]/(X^2) who´s minimum homogenous weight is 440.

Homogenous weight enumerator: w(x)=1x^0+196x^440+112x^444+616x^447+3052x^448+1624x^450+1120x^451+3304x^452+3808x^455+8568x^456+8568x^458+3360x^459+8232x^460+5040x^463+12642x^464+31752x^466+11424x^467+23352x^468+11872x^471+22575x^472+44072x^474+12768x^475+22344x^476+7336x^479+13482x^480+252x^488+287x^496+147x^504+147x^512+70x^520+21x^528

The gray image is a linear code over GF(8) with n=536, k=6 and d=440.
This code was found by Heurico 1.16 in 16.5 seconds.