Can a puffy jennyfer j jacket be washed in the washing machine?

I have a white :/ puffy Jennyfer j jacket and the tag on the side says not to wash, bleach, iron or dry clean it says specialist clean only, but I don't want to take it in because I've only wear it a few times and I take care of it but I took it to school and it got some stains from like the pencil writings that were on the table I was sitting at(dirty from the sleaves) and like I was wondering If I could just throw it in the washing machine and hang it to let it dry or buy some type of chemical to clean it and would it damage it or something?