The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  X  1  1  X  1  1  X  1  1  1  1 a*X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  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 a^7*X+a^6 a^7*X+1 a^7*X+a^2 a^3 a^7*X+2  1  0 a^7*X+a^6 a^7 a^5 a^3  a a^7*X+2 a^7*X+a^2 X+a^7 a^7*X+1  X  1 a^6*X+2 a^6*X+a^2 a^7*X+1 a^6*X+a^6 X+a a^6*X+2 a*X a^2*X+a  1 a^6*X+1 a^6*X+a^2  1 X+a^3 2*X+a  1 X+a^7 X+a^5 a^6*X+a^6 a^2*X+a^7  1 X+a^5 a^6*X+2 2*X+2 X+a^7 a^5*X+a^6 X+a^3 X+a^5 2*X+1 a^2*X+a^3 a^7*X+2 a^5*X+a^5 a^2*X+a^7 a^3*X+a  a 2*X+a a^5*X+a X+a^7 a^3*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  0 a^5*X a^3*X a^6*X 2*X a^3*X  0 a^5*X a^3*X a^5*X a^3*X 2*X a*X a^2*X a^5*X a^7*X a*X  X a^2*X  0 a^6*X  0 a^3*X 2*X  X a*X a^5*X 2*X  0  X a^2*X a^5*X a^6*X a^6*X a^5*X a^2*X  X a^5*X a*X 2*X  0 a^2*X a*X a^7*X a^3*X  0  X 2*X  0 a^6*X a^6*X a^3*X a^7*X a*X a^6*X  0 a^6*X a^6*X  X
 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*X a^2*X a^7*X  0 a^3*X a*X a^3*X a^6*X a^6*X 2*X a^3*X a*X  X  X a^5*X a*X  0  0 a^6*X a^6*X 2*X a^5*X 2*X a^6*X a^3*X a*X a^7*X 2*X a^6*X 2*X a*X  0 a^6*X a^3*X a*X 2*X a^2*X a^3*X a^3*X 2*X a^5*X a^5*X 2*X  X  0  X  X a^2*X 2*X a^7*X  X  0  0 a^2*X a^2*X  0 a^5*X  0 a^5*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+152x^540+72x^546+648x^548+1496x^549+720x^550+648x^554+5184x^555+8712x^557+4616x^558+4968x^559+4536x^563+22896x^564+24408x^566+10632x^567+9936x^568+18144x^572+78336x^573+62424x^575+21584x^576+20664x^577+29160x^581+103464x^582+61272x^584+18768x^585+16200x^586+616x^594+400x^603+352x^612+248x^621+112x^630+72x^639

The gray image is a linear code over GF(9) with n=648, k=6 and d=540.
This code was found by Heurico 1.16 in 43.6 seconds.