The generator matrix

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

generates a code of length 62 over F8[X]/(X^2) who´s minimum homogenous weight is 408.

Homogenous weight enumerator: w(x)=1x^0+441x^408+224x^409+392x^410+616x^411+560x^415+3906x^416+2968x^417+4368x^418+2352x^419+2800x^423+11347x^424+8568x^425+9632x^426+5376x^427+10640x^431+34328x^432+23240x^433+23408x^434+11984x^435+14672x^439+38878x^440+22344x^441+19544x^442+8344x^443+420x^448+315x^456+182x^464+147x^472+91x^480+56x^488

The gray image is a linear code over GF(8) with n=496, k=6 and d=408.
This code was found by Heurico 1.16 in 14.8 seconds.