The generator matrix

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

generates a code of length 46 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+258x^44+96x^46+99x^48+54x^52+4x^56

The gray image is a linear code over GF(2) with n=184, k=9 and d=88.
As d=89 is an upper bound for linear (184,9,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 9.
This code was found by Heurico 1.16 in 0.675 seconds.