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

generates a code of length 37 over Z3[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+162x^72+324x^74+216x^75+18x^78+6x^81+2x^108

The gray image is a linear code over GF(3) with n=333, k=6 and d=216.
This code was found by Heurico 1.16 in 0.0162 seconds.