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

generates a code of length 72 over F9[X]/(X^2) who´s minimum homogenous weight is 540.

Homogenous weight enumerator: w(x)=1x^0+176x^540+976x^549+1112x^558+648x^560+872x^567+10368x^569+984x^576+41472x^578+728x^585+520x^594+384x^603+432x^612+184x^621+128x^630+56x^639+8x^648

The gray image is a linear code over GF(9) with n=648, k=5 and d=540.
This code was found by Heurico 1.16 in 1.53 seconds.