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

generates a code of length 62 over F8[X]/(X^2) who´s minimum homogenous weight is 424.

Homogenous weight enumerator: w(x)=1x^0+4228x^424+6272x^426+5432x^432+1792x^434+8694x^440+6272x^442+49x^448+14x^456+14x^464

The gray image is a linear code over GF(8) with n=496, k=5 and d=424.
This code was found by Heurico 1.16 in 0.811 seconds.