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

generates a code of length 41 over Z3[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+58x^81+6x^84+6x^87+8x^90+2x^99

The gray image is a linear code over GF(3) with n=123, k=4 and d=81.
As d=81 is an upper bound for linear (123,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.00533 seconds.