Of course, the first thing to do is take the tube out and check the tire for sharp fragments that are still stuck in it. I didn't feel anything, but as I was turning it and feeling, I heard a sound of something sliding inside the tire.
Here's what I found:
Two pieces of glass, or as we geologists call it "beerbottleite".
So I looked over the tube, eventually I have found six punctures. Four of the punctures were in pairs where the glass went through both sides of the tube. The two others were pin holes.
So now, I'm all patched up, and hoping that I've found all of them.