The generator matrix

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

generates a code of length 37 over Z3[X]/(X^2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+54x^74+12x^75+12x^78+2x^81

The gray image is a linear code over GF(3) with n=111, k=4 and d=74.
As d=74 is an upper bound for linear (111,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.13 in 0.00535 seconds.