Not sure of the height of the stock heatsink, plus they have a couple different kinds...though its a K so probably a "full size".
One doc I have lists ~81mm for LGA115x stock design, but that seems a bit tall, could be the 'keep out' size instead.
There are a couple nice LP coolers, though many are not technically rated for a 77W TDP. If you are not overclocking and the case has decent airflow they can do fine.
Measure the clearance you're working with first, can't really recommend anything without that.
Nearly dead silent HTPC ver 2.0: i3-4340 w/ Noctua NH-L9i on Z87E-itx inside CM130 elite, fanless PSU, SSD OS drive
SAN shares via 40GbE tunneled over 56Gb infiniband links
microcenter & ebay = severe risks to my wallet