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

generates a code of length 69 over F8[X]/(X^2) who´s minimum homogenous weight is 456.

Homogenous weight enumerator: w(x)=1x^0+357x^456+819x^464+665x^472+574x^480+28672x^483+490x^488+357x^496+280x^504+175x^512+168x^520+126x^528+49x^536+28x^544+7x^552

The gray image is a linear code over GF(8) with n=552, k=5 and d=456.
This code was found by Heurico 1.16 in 0.741 seconds.