The generator matrix

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

generates a code of length 47 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+14x^50+1x^52

The gray image is a linear code over GF(2) with n=188, k=4 and d=100.
As d=100 is an upper bound for linear (188,4,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 4.
This code was found by Heurico 1.16 in 0.0325 seconds.