The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  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  X  1  1  X a^2*X  1  1  1  1  1
 0  1  1  a a^7*X+a^2 a^3 a^7*X+2 a^7*X+a^6 a^5 a^7  0 a^7 a^5 a^7*X+a^6 a^3  1  a a^7*X+a^2 a^7*X+1  1  0 a^5 a^7*X+a^6 a^7*X+2 a^7  X a^3 a^7*X+2 X+a^5 a^7*X+a^2 a^6*X+a^2 a^5*X+a^2 a^6*X+a^2 X+a^3  X X+a^3  a X+a a^3*X a^6*X+a^6 X+a a^6*X+2 X+a^7 a*X+a^5 a^5*X+a^6 a^7*X+a^6  1 a*X+a^3 X+a^7  1  1 a^6 a^2*X+a^6 a^6*X+a^2 a^7*X+1  0
 0  0 a^7*X  0 a^7*X  X a^6*X a^6*X 2*X a*X a^7*X a*X  X a*X  X  X a^6*X 2*X a^7*X a^7*X a*X  X a*X  0 2*X a^3*X a^3*X  X a^3*X a^5*X 2*X a^6*X  0 a^2*X a^2*X a^7*X a*X 2*X a^6*X  0  X  0 a^2*X  0 a^5*X a^3*X 2*X a*X 2*X a^6*X  0 a^2*X  0 a^2*X a*X  X
 0  0  0  X a^7*X a^7*X  X a*X  X a^2*X a^5*X a^6*X a^5*X a^3*X  0 a^6*X a^2*X a^7*X a*X 2*X  X a*X a^5*X a^5*X a^2*X a^7*X  0 a^2*X a^3*X  X 2*X  0 a^6*X a^2*X a^5*X a^5*X a^2*X a^3*X  0 a^3*X  X a^6*X a^6*X  X a^7*X a^6*X  0 a^7*X  0 a*X a^5*X a^3*X a^7*X a^2*X  0 a^6*X

generates a code of length 56 over F9[X]/(X^2) who´s minimum homogenous weight is 414.

Homogenous weight enumerator: w(x)=1x^0+192x^414+360x^419+216x^420+968x^423+72x^424+288x^425+2160x^426+2880x^427+3888x^428+2952x^429+1120x^432+1728x^433+3024x^434+12960x^435+10800x^436+13392x^437+7992x^438+1040x^441+13824x^442+16416x^443+55080x^444+39744x^445+41760x^446+20952x^447+904x^450+36864x^451+32760x^452+87264x^453+51552x^454+45576x^455+20376x^456+720x^459+680x^468+440x^477+352x^486+128x^495+16x^504

The gray image is a linear code over GF(9) with n=504, k=6 and d=414.
This code was found by Heurico 1.16 in 31.9 seconds.