Another faceless jigsaw

Question

Start with a square. Any side of the square can be either straight or have an interlocking pattern, as shown in the two examples below:

That gives $2 \times 2 \times 2 \times 2 = 16$ possible squares.

Is it possible to create a $4 \times 4$ jigsaw puzzle (outside borders straight) with these $16$ pieces? Rotation or flipping of pieces is not allowed.

Answer 1

I think this has them all:

+---+---+---+---+
| 2 % 3 % 2 | 1 |
+-%-+-%-+-%-+-%-+
| 3 % 4 % 3 % 3 |
+-%-+-%-+---+-%-+
| 2 % 2 | 0 | 2 |
+---+---+---+-%-+
| 1 % 2 % 1 | 1 |
+---+---+---+---+

I went with % for the interlocking pattern sides, and the number is how many of those sides a given square has.

Answer 2

Here is an alternative solution that has a bit more structure to it:

+---+---+---+---+
|   %   %   |   |
+-%-+-%-+-%-+-%-+
|   %   %   |   |
+-%-+-%-+-%-+-%-+
|   %   %   |   |
+---+---+---+---+
|   %   %   |   |
+---+---+---+---+

Looking at the 5 horizontal lines, there are 4 adjacent pairs, and each combination occurs exactly once. The same goes for the vertical lines. Therefore all the tiles are different, and every combination of four sides occurs exactly once.