The generator matrix

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

generates a code of length 40 over Z2[X]/(X^3) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+3x^40+24x^41+3x^42+1x^50

The gray image is a linear code over GF(2) with n=160, k=5 and d=80.
As d=81 is an upper bound for linear (160,5,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 5.
This code was found by Heurico 1.16 in 0.0177 seconds.