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

generates a code of length 38 over Z3[X]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+54x^76+18x^78+8x^81

The gray image is a linear code over GF(3) with n=114, k=4 and d=76.
As d=76 is an upper bound for linear (114,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.00766 seconds.