The generator matrix

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

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+91x^8+120x^9+136x^10+48x^11+90x^12+24x^13+2x^16

The gray image is a linear code over GF(2) with n=40, k=9 and d=16.
As d=16 is an upper bound for linear (40,9,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 9.
This code was found by Heurico 1.11 in 0.016 seconds.