@RWB Unfortunately the camera you linked doesn’t send the picture over I2C. It has two interfaces: MIPI CSI (high-speed serial differential data, this is what the Raspberry Pi uses) and an 8-bit parallel output (which you could hook to D0 to D7 on the Core). I2C is used to control the camera itself, tell it when to take a picture, what format it should be output as, set focus, enable/disable a flash, stuff like that.
I suppose one option would be to use the 8-bit output hooked to a Shift Register and connect that to the SPI port of the Core. That’s still a pretty high resolution, so even with JPEG compression you’d need some SPI based SRAM to hold the image so it could be uploaded/emailed/MMSed. That would make it even slower since you’d have to share the SPI port with the Shift Register and SRAM, basically reading a byte from the camera, writing it to the SRAM, sending an I2C write to tell the camera to send the next byte, rinse, lather, repeat.
The Core is just not designed to work with a large megapixel camera.
Your best bet is to either use a UART camera or get a cheap WiFi webcam and program the Core to talk to it via TCP (basically instruct it to snap a picture and post it to a specific URL).