The generator matrix

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

generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+12x^30+1x^32+2x^36

The gray image is a linear code over GF(2) with n=116, k=4 and d=60.
As d=61 is an upper bound for linear (116,4,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 4.
This code was found by Heurico 1.16 in 0.00543 seconds.