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  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  X  X a*X a^2*X a^4*X a^5*X a^5*X  X a^5*X a^6*X  0 a*X a^5*X a*X a^5*X a^6*X a^6*X a^2*X a*X a*X  0 a^3*X a^4*X a^5*X a^3*X a^2*X a^5*X  0 a^6*X a^4*X a^2*X a^5*X a^4*X a^3*X a^4*X a^2*X  X a*X a*X a^5*X  X a^4*X a^4*X a^4*X  X  X a^4*X  0 a^2*X  0 a*X a*X  X a*X a^2*X a^5*X  X a^5*X a^6*X a^2*X  X a*X  0
 0  0  X  0 a^6*X a^5*X a*X a^6*X a^6*X a*X a^6*X a^2*X a*X a^3*X  X a^5*X a^3*X a^4*X a^4*X  X a^4*X  0  X a*X a*X a^6*X  0 a^3*X a^6*X  X a^2*X a^6*X a*X a^5*X a*X a^2*X  0 a*X a^6*X a^3*X a^3*X a^3*X  X a*X a^5*X a^4*X a^4*X  0 a^2*X a*X  X  X  X a^6*X a*X a^3*X a*X a^2*X a^5*X  X  0 a^5*X  X a^6*X a^4*X a^6*X  0
 0  0  0  X  X a^4*X a^4*X  X a^6*X a^4*X a^6*X a^6*X a^3*X a*X a^4*X a*X  0  0 a^6*X a^5*X a^6*X a^5*X a^5*X  X  X  X a^5*X a*X  0 a^4*X a^4*X a*X  X a*X a^5*X a^5*X  0 a*X a^5*X a^4*X a^6*X a^4*X a^6*X a^5*X  X a*X  0 a^3*X a^3*X  0 a^5*X a^6*X a*X a^6*X a*X  0 a^4*X a*X  X a^4*X a^3*X  0  X a^6*X a*X a^5*X a^3*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+203x^440+714x^448+749x^456+3584x^462+707x^464+25088x^470+399x^472+357x^480+329x^488+224x^496+210x^504+98x^512+70x^520+35x^528

The gray image is a linear code over GF(8) with n=536, k=5 and d=440.
This code was found by Heurico 1.16 in 0.723 seconds.