The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  X  1 a*X  1  1  1 a^5*X  1  1  1  X  1  1  1 a^7*X  1  1  0  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 a^7*X+2 a^7 a^7*X+a^6 a^7*X+a^2 a^3  1  a a^7*X+1 a^6*X+a^6 a^7*X+1 X+a^3 a^6*X+a^2 a^5*X+1  0 X+a a^2*X+a  1 a^6*X+a^6  1 a^7*X+2 X+1 a*X+a^3  1 a^5*X+a^2 2*X+a^2 a^5  1 a^6*X+1 a^6*X+2 X+a^7  1 a^5*X+1 X+a^5  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^2*X a^6*X 2*X  0 a*X 2*X 2*X  X a*X a^5*X a^3*X a^5*X a^2*X a^3*X a^2*X a^7*X 2*X a^2*X a^2*X 2*X  X a*X  X a^7*X a^6*X  0 a^7*X a^6*X 2*X a^5*X  0 a^6*X  0 a^2*X  0
 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 a^2*X a^5*X a*X a^6*X 2*X  0 a^2*X a*X  0 a^6*X a^7*X  X 2*X a^5*X a^6*X a^6*X a^5*X a^5*X  0 a^3*X  0 a^2*X  X  X 2*X a*X a*X 2*X a^7*X 2*X a^6*X a*X 2*X a^3*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+136x^396+72x^400+216x^404+1264x^405+2016x^409+2160x^410+1368x^411+2880x^413+4872x^414+14256x^418+12960x^419+5616x^420+8208x^422+10280x^423+58464x^427+55080x^428+19656x^429+20736x^431+21728x^432+135144x^436+87264x^437+25848x^438+20448x^440+18952x^441+768x^450+480x^459+368x^468+192x^477+8x^486

The gray image is a linear code over GF(9) with n=486, k=6 and d=396.
This code was found by Heurico 1.16 in 30.4 seconds.