The generator matrix

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

generates a code of length 45 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+81x^44+96x^45+72x^46+3x^48+3x^60

The gray image is a linear code over GF(2) with n=180, k=8 and d=88.
As d=88 is an upper bound for linear (180,8,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 8.
This code was found by Heurico 1.16 in 0.0325 seconds.