The generator matrix

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

generates a code of length 62 over F8[X]/(X^2) who´s minimum homogenous weight is 417.

Homogenous weight enumerator: w(x)=1x^0+2296x^417+9688x^418+1848x^419+560x^423+42x^424+17808x^425+39760x^426+6664x^427+1120x^431+308x^432+23352x^433+52696x^434+5320x^435+1904x^439+147x^440+31808x^441+59136x^442+7672x^443+7x^456+7x^496

The gray image is a linear code over GF(8) with n=496, k=6 and d=417.
This code was found by Heurico 1.16 in 12 seconds.