The generator matrix

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

generates a code of length 54 over F9[X]/(X^2) who´s minimum homogenous weight is 396.

Homogenous weight enumerator: w(x)=1x^0+112x^396+864x^405+1048x^414+1008x^423+5832x^424+936x^432+46656x^433+840x^441+696x^450+496x^459+368x^468+152x^477+40x^486

The gray image is a linear code over GF(9) with n=486, k=5 and d=396.
This code was found by Heurico 1.16 in 1.09 seconds.