As you have an iPhone - and assuming that both iPad and iPhone are signed-in to iCloud with the same AppleID - to send and receive SMS/MMS messages (green bubbles) from your iPad (including receive SMS codes for AutoFill by your iPad) you must explicitly enable Text Message Forwarding for your iPad on your iPhone...
On your iPhone:
Settings > Messages > Text Message Forwarding - set to ON - and explicitly enable your iPad from the list of devices.
Also ensure that Messages in iCloud is enabled on both your iPhone and iPad:
Settings > [Your Name / AppleID] > Messages - set to ON