The generator matrix

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

generates a code of length 32 over Z2[X]/(X^3) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+14x^34+1x^36

The gray image is a linear code over GF(2) with n=128, k=4 and d=68.
As d=68 is an upper bound for linear (128,4,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 4.
This code was found by Heurico 1.16 in 0.00779 seconds.