Saw this in my garden the other day, seemingly laying eggs. It was about 2" long and i believe had wings. When it slightly opened its back there was a bright blue streak of colour.
I have no idea what this is, but would be interested to know.
I checked this with our county beetle recorder who confirmed that it was a ground beetle (family Carabidae) possibly in the genus Carabus. Those are indeed eggs as you thought. It looks as if the beetle has been squashed and the eggs have burst out of its abdomen rather than it egg-laying in a normal fashion.