The generator matrix

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

generates a code of length 37 over Z3[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+24x^73+198x^74+12x^76+4x^78+2x^84+2x^93

The gray image is a linear code over GF(3) with n=333, k=5 and d=219.
This code was found by Heurico 1.16 in 0.0105 seconds.