Timing chain tensioner failure in your 2014 Audi A4 at 150,000 miles is a well-documented concern with the EA888 2.0T engine. The tensioner maintains chain tension, and its failure can lead to catastrophic engine damage.
The EA888 Tensioner Issue
Earlier EA888 engines (2008-2013) had problematic tensioners that Audi updated. Your 2014 likely has the revised design, but at 150,000 miles, even improved tensioners can wear. The timing chain also stretches, working in combination with tensioner wear.
How Tensioner Failure Occurs
The hydraulic tensioner maintains chain tension using oil pressure. Internal valving prevents the tensioner from collapsing when the engine is off. When this mechanism fails, the tensioner can collapse during shutdown, and on restart, the slack chain can jump timing.
Code P0014 Connection
P0014 indicates exhaust camshaft timing is over-advanced. A worn tensioner allows chain slack, permitting the camshaft to drift from commanded timing. This code with chain rattle strongly suggests tensioner/chain wear.
Critical Urgency
Timing tensioner failure can allow the chain to jump timing, causing pistons to strike valves in this interference engine. The result is bent valves and potentially catastrophic damage. Rattling on cold start is a warning that shouldn't be ignored.