The generator matrix

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

generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+212x^20+136x^22+114x^24+40x^26+8x^28+1x^32

The gray image is a linear code over GF(2) with n=88, k=9 and d=40.
As d=40 is an upper bound for linear (88,9,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 9.
This code was found by Heurico 1.11 in 0.078 seconds.