Keep your images and MMS size to less than 300kb, that's the limit for MMS. So you may have to downscale them, increase JPG compression, crop them, or whatever you need to do to reduce their sizes.
It's actually quite a frequent problem for MMS and modern large screen smart-phones with their multi-megapixel cameras. MMS was introduced during the era of flip-phones, and the specification has never been updated, it's legacy.