The generator matrix

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

generates a code of length 10 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+51x^8+32x^9+88x^10+32x^11+50x^12+2x^16

The gray image is a linear code over GF(2) with n=40, k=8 and d=16.
As d=16 is an upper bound for linear (40,8,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 8.
This code was found by Heurico 1.16 in 0.000626 seconds.