The generator matrix

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

generates a code of length 41 over Z2[X]/(X^3) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+28x^42+2x^44+1x^48

The gray image is a linear code over GF(2) with n=164, k=5 and d=84.
As d=84 is an upper bound for linear (164,5,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 5.
This code was found by Heurico 1.16 in 0.0197 seconds.