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  1  1  1  1  1  1  1  1  X  1  1  X  X  1  X  1  1  1  X  1  1  1  X  1  1  1  1  1
 0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 X^2 2X^2 2X^2  0 2X^2  0  0 X^2 2X^2 X^2 2X^2 2X^2 X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2 2X^2  0 2X^2 2X^2  0  0  0  0
 0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 2X^2 X^2  0 X^2 2X^2 2X^2 2X^2  0  0 X^2 X^2 2X^2 X^2 X^2 2X^2 X^2 X^2  0 2X^2 X^2 2X^2 2X^2  0  0 X^2 2X^2 2X^2 X^2  0 X^2  0 2X^2  0  0  0 X^2  0  0
 0  0  0 X^2  0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2  0 X^2 2X^2  0  0  0 2X^2 2X^2 X^2  0 2X^2 X^2  0 2X^2 2X^2  0 X^2 2X^2  0  0 X^2 2X^2 2X^2  0 X^2  0 X^2  0  0 2X^2 2X^2 X^2 2X^2 X^2  0  0
 0  0  0  0 X^2  0  0 X^2 2X^2  0 2X^2 2X^2 X^2 X^2 X^2 2X^2 X^2 X^2  0 2X^2 X^2 2X^2 2X^2 2X^2 X^2  0 2X^2 X^2 X^2  0  0 2X^2  0 2X^2 X^2 2X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2  0
 0  0  0  0  0 X^2  0 2X^2 2X^2 X^2  0 2X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 X^2 2X^2 2X^2  0 X^2 X^2 2X^2  0 2X^2 2X^2 2X^2  0  0 X^2 2X^2  0  0 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2  0
 0  0  0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2 X^2  0 X^2 X^2  0  0 X^2 2X^2 X^2 X^2 X^2 X^2  0 2X^2 2X^2  0 X^2 2X^2  0 X^2  0 2X^2 X^2 X^2 X^2 X^2  0 2X^2 X^2  0  0  0  0  0 2X^2 X^2 X^2 X^2 X^2  0

generates a code of length 51 over Z3[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+38x^84+138x^87+192x^90+300x^93+648x^96+1134x^99+14680x^102+1448x^105+560x^108+138x^111+170x^114+116x^117+68x^120+26x^123+20x^126+4x^129+2x^135

The gray image is a linear code over GF(3) with n=459, k=9 and d=252.
This code was found by Heurico 1.16 in 2.38 seconds.