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

generates a code of length 67 over F8[X]/(X^2) who´s minimum homogenous weight is 424.

Homogenous weight enumerator: w(x)=1x^0+546x^424+1568x^432+2730x^440+3164x^448+3584x^455+3633x^456+50176x^463+3864x^464+175616x^471+4172x^472+4312x^480+3696x^488+2660x^496+1610x^504+595x^512+189x^520+28x^528

The gray image is a linear code over GF(8) with n=536, k=6 and d=424.
This code was found by Heurico 1.16 in 43.5 seconds.