Yes, the larger an image, the more fine-grained patterns it contains, thus the more accurate one’s model would be. Beware though, as there is a diminishing return, and it is better to scale both the input resolution and model size than either one alone.
224, I believe, comes from the AlexNet paper, which cropped 224 X 224 patches out of 256 X 256 images as a form of data augmentation (there are more details in the paper. I highly suggest reading it.). To the best of my knowledge, there is no specific reason they settled with 224 other than that it offered a compromise between memory/time and accuracy.
Other popular dimensions, like 460 X 460, have the same story: There is no rationale behind them per se, except that for most datasets (most being the operative word, since some applications, like medical imaging, often requires very high-resolution images, whereas in other cases, like digit recognition, you can get away with 28 X 28 images), they’re the sweet spot between not too large as to make training them a pain, but big enough to contain valuable information. A few are 96 X 96, 128 X 128, 156 X 156, 160 X 160, 192 X 192, 224 X 224, 256 X 256, 288 X 288, 300 X 300, 396 X 396, 460 X 460, 512 X 512, 800 X 800, 1024 X 1024, and so on (yet another reason for these particular values, which are all multiples of 32, is that powers of two are extremely common in deep learning and computer science in general.).
Finding the maximum dimensions in your dataset can be done easily with ImageMagick, but please bear in mind you should test out smaller sizes first to ensure you’re not wasting computation time & power for a 0.001% increase in score.
Have a great weekend!