the best way (for me) to make it it's the next infrastructure:
<form method="POST">
<input type="submit" formaction="default_url_when_press_enter" style="visibility: hidden; display: none;">
<!-- all your inputs -->
<input><input><input>
<!-- all your inputs -->
<button formaction="action1">Action1</button>
<button formaction="action2">Action2</button>
<input type="submit" value="Default Action">
</form>
with this structure you will send with enter a direction and the infinite possibilities for the rest of buttons.