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  X  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  X  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  0  0  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  0 a^5*X  0

generates a code of length 55 over F9[X]/(X^2) who´s minimum homogenous weight is 405.

Homogenous weight enumerator: w(x)=1x^0+168x^405+968x^414+976x^423+648x^424+1088x^432+10368x^433+848x^441+41472x^442+824x^450+680x^459+496x^468+336x^477+136x^486+40x^495

The gray image is a linear code over GF(9) with n=495, k=5 and d=405.
This code was found by Heurico 1.16 in 1.13 seconds.