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

generates a code of length 57 over F9[X]/(X^2) who´s minimum homogenous weight is 436.

Homogenous weight enumerator: w(x)=1x^0+4824x^436+6264x^437+216x^440+824x^441+2160x^442+7920x^443+12816x^444+35208x^445+25560x^446+648x^448+3456x^449+4800x^450+8640x^451+19800x^452+21024x^453+64800x^454+44136x^455+5832x^456+5184x^457+13824x^458+12408x^459+18360x^460+36432x^461+36144x^462+87624x^463+52344x^464+88x^468+40x^477+24x^486+24x^495+8x^504+8x^513

The gray image is a linear code over GF(9) with n=513, k=6 and d=436.
This code was found by Heurico 1.16 in 27.9 seconds.