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

generates a code of length 54 over F9[X]/(X^2) who´s minimum homogenous weight is 412.

Homogenous weight enumerator: w(x)=1x^0+4536x^412+6192x^413+160x^414+360x^416+1296x^417+2520x^418+5544x^419+10224x^420+34344x^421+22320x^422+256x^423+2592x^424+5760x^425+9072x^426+10512x^427+14832x^428+18432x^429+62856x^430+40464x^431+80x^432+20736x^433+23040x^434+24624x^435+21960x^436+26280x^437+29664x^438+84888x^439+47664x^440+64x^441+48x^450+48x^459+40x^468+32x^477

The gray image is a linear code over GF(9) with n=486, k=6 and d=412.
This code was found by Heurico 1.16 in 25.4 seconds.