The Oslo Method has been applied to particle-$gamma$ coincidences following the $^{239}mathrm{Pu}$(d,p) reaction to obtain the nuclear level density (NLD) and $gamma$-ray strength function ($gamma$SF) of $^{240}mathrm{Pu}$. The experiment was conducted with a 12 MeV deuteron beam at the Oslo Cyclotron Laboratory. The low spin transfer of this reaction leads to a spin-parity mismatch between populated and intrinsic levels. This is a challenge for the Oslo Method as it can have a significant impact on the extracted NLD and $gamma$SF. We have developed an iterative approach to ensure consistent results even for cases with a large spin-parity mismatch, in which we couple Greens Function Transfer calculations of the spin-parity dependent population cross-section to the nuclear decay code RAINIER. The resulting $gamma$SF shows a pronounced enhancement between 2-4 MeV that is consistent with the location of the low-energy orbital $M1$ scissors mode.