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

generates a code of length 37 over Z3[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+190x^66+342x^69+1910x^72+3568x^75+240x^78+212x^81+76x^84+12x^87+8x^90+2x^108

The gray image is a linear code over GF(3) with n=333, k=8 and d=198.
This code was found by Heurico 1.16 in 0.147 seconds.