The generator matrix

1 X^2 1 1 X^2+X 1 0 1 X^2+X 1 X^2+X 1 1 X^2+X X^2+X X^2+X 1 1 X^2 1 1 X^2 1 1 1 0 X X^2+X 1 X X 0 1 0 0 1 1 1 X^2+X 1 X 1 1 X^2+X 1 X^2+X
X+1 1 X^2+X X 1 1 X^2+X 0 1 X^2+1 1 X+1 0 X^2+X 1 X^2 X^2+1 0 X^2 X^2+X X^2+X+1 1 0 X 1 1 1 1 X^2+X+1 X^2 X^2+X X 1 1 X X 0 0 1 X^2+X X^2+X X^2+1 1 1 1 X^2
0 0 X^2 1 X^2+X+1 1 1 X^2 0 0 X 1 1 1 1 1 X^2+X X+1 1 X^2+X+1 X X 0 X^2 X^2+1 X X+1 X^2+1 1 X^2 X^2+X X^2+X X+1 1 1 X^2+1 X^2+X+1 X^2+X X+1 X^2+X 0 X^2 0 X X^2+1 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+322x^44+127x^48+46x^52+16x^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 an older version of Heurico in 0 seconds.