The generator matrix

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

generates a code of length 72 over F9[X]/(X^2) who´s minimum homogenous weight is 557.

Homogenous weight enumerator: w(x)=1x^0+7632x^557+11624x^558+7488x^559+72x^560+1296x^562+5040x^563+5400x^564+5976x^565+39024x^566+33760x^567+19584x^568+1152x^569+5184x^571+12600x^572+8640x^573+6192x^574+59760x^575+50216x^576+29088x^577+4608x^578+11016x^580+23184x^581+15120x^582+11160x^583+74376x^584+56624x^585+25488x^586+40x^594+56x^603+24x^612+8x^630+8x^639

The gray image is a linear code over GF(9) with n=648, k=6 and d=557.
This code was found by Heurico 1.16 in 38.9 seconds.