Why would I still get ping replies when I set TTL to 2?

I am trying to build a traceroute program and started by testing pings with different ttl values.

Ping 8.8.8.8 with TTL 1, I get a TTL exceeded message from my gateway, as expected.

Ping with TTL 2, I get a response from 8.8.8.8.

Ping with TTL 3, I get another TTL exceeded message from an Internet router.

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Why am I getting a response with TTL 2?