The generator matrix

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

generates a code of length 20 over F9[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+112x^144+248x^153+5832x^160+176x^162+56x^171+136x^180

The gray image is a linear code over GF(9) with n=180, k=4 and d=144.
This code was found by Heurico 1.16 in 0.00536 seconds.