Hardwire connection

You won't necessarily get a better ping time when switching to wired as your connection is still at the same number of hops. The wired connection will be better performance wise because it won't be subjected to wireless interferance from other WiFi devices
which can reduce your available throughput on the WiFi channel.

Try restarting your router and clearing your xbox cache. When I swapped from wireless to hardwired the difference was quite significant.

As Crumb Snatcherz said above "reset your router and clear the xbox cache". I switch between wired and wireless a lot depending on what I'm doing.

How many people in your household are using the same internet while you game? People confuse fast internet with strong internet all the time. If your ping is spiking it may be because other people are doing stuff too which is causing you to spike periodically.

Can your router block the Xbox x hardwire?