As with Dmitry, I assume you are applying a 4-bit s-box to a 4-by-4 array of 16 bits, first to the rows (after xoring 16 bits of key material to the plaintext), then to the columns (and lastly xoring 16 more bits of key material to produce the ciphertext). Strictly speaking, you need to specify the 4-bit s-box in order to fully evaluate it against differential cryptanalysis, though I can tell you right now the construction will be extremely weak no matter which such s-box you choose. In fact, you can choose 8 distinct s-boxes (instead of using the same one 8 times) and that won't make any difference to the strength of the construction.
First, if only one of the 'row-wise' s-boxes is differentially 'active' then the attacker can immediately and directly read the output difference of that active row-wise s-box merely by looking at which column-wise s-boxes are differentially active (which you can tell just by looking at the resulting ciphertext pairs). In the same way, if only one row-wise s-box is active at a time you also immediately know the input and output differences for any active column-wise s-box (they'll each have only one active input bit -- the one coming from the active row-wise s-box).
Now, if you know the input and output differences for a given s-box for sufficiently many pairs of texts (which for 4-bit s-boxes may only be two or three pairs) then it is trivial to deduce the key bits standing between the attacker and the active s-box in question. My guess is that it would take no more than 16 chosen plaintexts to recover the entire key -- four per row-wise s-box. Each such quartet of plaintexts would vary in only one row, giving the attacker six differential pairs to play with (four distinct texts can be paired in six ways). I won't bother to speculate how long it would take to deduce the full 32 key bits, but I suspect one could do it by hand with pen and paper in less time than it took me to write this answer.