The generator matrix

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

generates a code of length 54 over F9[X]/(X^2) who´s minimum homogenous weight is 429.

Homogenous weight enumerator: w(x)=1x^0+3888x^429+720x^432+1944x^438+8x^486

The gray image is a linear code over GF(9) with n=486, k=4 and d=429.
This code was found by Heurico 1.16 in 0.0206 seconds.