The generator matrix

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

generates a code of length 11 over Z2[X]/(X^3) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+44x^9+58x^10+80x^11+22x^12+28x^13+14x^14+8x^15+1x^16

The gray image is a linear code over GF(2) with n=44, k=8 and d=18.
As d=19 is an upper bound for linear (44,8,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 8.
This code was found by Heurico 1.16 in 0.00072 seconds.