The generator matrix

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

generates a code of length 26 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+24x^26+2x^28+4x^30+1x^32

The gray image is a linear code over GF(2) with n=104, k=5 and d=52.
As d=52 is an upper bound for linear (104,5,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 5.
This code was found by Heurico 1.16 in 0.00376 seconds.