The generator matrix

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

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+103x^20+64x^22+78x^24+8x^28+1x^32+1x^36

The gray image is a linear code over GF(2) with n=88, k=8 and d=40.
As d=41 is an upper bound for linear (88,8,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 8.
This code was found by Heurico 1.16 in 1.98 seconds.