The generator matrix

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

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+47x^44+32x^45+40x^46+5x^48+2x^56+1x^60

The gray image is a linear code over GF(2) with n=180, k=7 and d=88.
As d=89 is an upper bound for linear (180,7,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 7.
This code was found by Heurico 1.16 in 0.0287 seconds.