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

generates a code of length 23 over F9[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+336x^144+2120x^153+4368x^162+7672x^171+13152x^180+472392x^184+16160x^189+11504x^198+3736x^207

The gray image is a linear code over GF(9) with n=207, k=6 and d=144.
This code was found by Heurico 1.16 in 26.9 seconds.