Standard text messaging has a REALLY small size limitation by today's standards as it's a really old protocol. Add to that the extra size needed for a .gif and it'll be quite difficult to get anything of any quality to go through. As suggested by @mustang7757's question, a messaging app that doesn't use the SMS protocol (which would require the recipient to be on the same app/platform) or messaging apps that can utilize RCS (you won't need to be on the same app but both devices need to support it and have it enabled) will be your best solution.