A few months late, but it might be because you called the this.context.getApplicationContext().getContentResolver().insert(Telephony.Mms.CONTENT_URI, mmsValues); before you added anything to the mmsValues variable, so it might've just inserted an empty ContentValues to the content resolver, so try moving that line to right above the smsManager.sendMultimediaMessage.
Also try these too.
https://github.com/klinker41/android-smsmms
https://github.com/aosp-mirror/platform_development/blob/master/samples/ApiDemos/src/com/example/android/apis/os/MmsMessagingDemo.java