Can adults beginners become great musicians?

When I began lerning and playing violin, I was 30 years old. I don't have any expectations I just began because I wanted for a very long time. I am still a very beginner because I improve very slowly. My violin teacher said adults beginners can improve faster than children but tey have a lot of matters children don't have, so it could ahve some difficulties children don't have to overcome.
As an adult, I can't dream of being part of a great orchestra but I enjoy every time I can play with some other beginners or in a small orchestra!
Enjoying music and playing is the most important thing but I 'd like to be better every day and someday be proud of my playing!
I know improving take time because it needs a lot of practice and I don't practice enough... with time, I hope I can become a great musician, playing in family meetings, at home for my children and husband, at school with the children, or with the other musicans!
I am really sure that loving music and take time to enjoy the instrument played and share with musicians or music lovers is the most important thing!
Some of adults beginners I know improve very fast and I enjoy their music with some jealousy !
Without wanting to be the best musician, becoming a great musician can be achieve by everyone even if the beginning come late! ^^