If you are doing a "don't fragment" ping then an 18000-byte ping should be dropped. The MTU is typically 1500 bytes.
If you are doing a ping that allows packet fragmentation, then perhaps you are experiencing an MTU squeeze. Perhaps you are using PPPoE and you're ISP only supports 1492 byte packets, and you need to lower your MTU.
To test this idea, try reducing the MTU on your test machine to something like 1400 bytes: