Comparator won't work
Assuming you're using a small (non-double) chest, try filling it like so:
Then set up your redstone roughly like this:
The comparator will output a signal with strength 1 if there are between 1 and 123 pieces of flesh in the chest, and strength 2 (or higher) if there are more. Putting 115 pieces of flesh in the chest means that five more pieces are needed to increase the strength. Once those five pieces are inserted, the repeater will activate, and power the door.