The generator matrix

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

generates a code of length 62 over Z3[X]/(X^2) who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+48x^123+162x^124+24x^126+4x^132+2x^135+2x^159

The gray image is a linear code over GF(3) with n=186, k=5 and d=123.
As d=123 is an upper bound for linear (186,5,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.0248 seconds.