The generator matrix

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

generates a code of length 64 over F8[X]/(X^2) who´s minimum homogenous weight is 437.

Homogenous weight enumerator: w(x)=1x^0+1120x^437+2352x^439+7952x^440+2240x^445+1568x^447+2534x^448+3808x^453+3248x^455+7903x^456+21x^464+21x^472

The gray image is a linear code over GF(8) with n=512, k=5 and d=437.
This code was found by Heurico 1.16 in 0.255 seconds.