Differential or Truncated Differential Attack On Small Cipher
How differential attack can be mounted with effort less than brute force.


Was the homework specifically to use a differential attack against this cipher?

Well, part of the problem you're having is that the cipher is, in some sense, too simple to use differential cryptanalysis against; the standard approach of "use DC to find a distinguisher in $N-1$ rounds, and then use that distinguisher to recover the subkey for the last round" doesn't apply.

The other issue is that you're still learning how to use differential cryptanalysis, and it certainly doesn't help that the standard approaches to use DC against this cipher doesn't work.

If you have to use DC, the first thing to do is look for high-probability differentials through the sbox; that is, values $\delta_i, \delta_o$ such that $sbox(x) \oplus sbox(x \oplus \delta_i) = \delta_o$ happen for lots of different values $x$; eyeballing the sbox, it would appear you can find such values which this happens far more often than a well-chosen sbox.

On the other hand, if you don't have to use DC, well, there's an easier approach to attack this cipher.  To start, we note that MDS matrices are bit-wise linear, and bit-wise linear functions have this property:

$$MDS(x \oplus y) = MDS(x) \oplus MDS(y)$$

for all values $x, y$.

Hint: how can you use this relation against the cipher?  How will this drastically reduce the work involved with attacking it?