How do I filter an audio signal that has 4 noise spikes in its Fourier transform?

Hi, I'm just a beginner in using Matlab, and my version is R2012b. We were provided, as an assignment, with an audio signal with its sampling frequency in a .mat file that I can play to see the signal (Handel's Hallelujah with constant noise). I can also use the wavwrite function to hear it outside of Matlab. Now, when I do an fft, I can see the plotted sound - with, however, 4 high spikes in the frequency spectral analysis.

I was asked to design a filter to remove the noise, and as an instruction that I should remove these spikes. How should I proceed to do this? First I've tried to set to 0 those parts of the Fourier transform that spiked, but that just distorted the signal. Then I've tried using the Filter Design toolbox to design a bandstop filter, but I didn't know how since we weren't yet introduced to it. What filter should I use and how?