The generator matrix

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

generates a code of length 19 over F9[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+152x^144+1008x^145+216x^146+1208x^153+3528x^154+432x^155+16x^162

The gray image is a linear code over GF(9) with n=171, k=4 and d=144.
This code was found by Heurico 1.16 in 0.00213 seconds.