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

generates a code of length 62 over F8[X]/(X^2) who´s minimum homogenous weight is 392.

Homogenous weight enumerator: w(x)=1x^0+826x^392+1869x^400+2905x^408+3556x^416+3584x^420+3591x^424+50176x^428+4466x^432+175616x^436+4347x^440+4067x^448+3563x^456+2149x^464+1092x^472+308x^480+28x^488

The gray image is a linear code over GF(8) with n=496, k=6 and d=392.
This code was found by Heurico 1.16 in 38.8 seconds.