According to Nintendo's Error Code Lookup, the 015-4404 error code may be due to some problem with the "Access Point", perhaps from being too far (over 30 feet) from the wireless router and/or some type of wireless interference form another electronic device such as a cordless phone or something.
So perhaps try making sure you are closer to your wireless router and (temporally) power down other nearby electronic devices to sse if your 3DS can then connect to Miiverse.
But if still no luck, perhaps you might want to give a call to Nintendo's 1-800-255-3700 (6 am ~ 7 pm Pacific, everyday) Customer Service number, and one of the service representatives can do some over the phone troubleshooting to determine exactly what the problem(s) might be, and then talk you through any needed steps to correct this.