I did gymnastics 16 hours/week and violin/orchestra for another 6ish hours/week, so I guess that's close enough for me to help. I averaged about 4 hours of homework per night in high school, and with mandatory before or after school study sessions for either constitutional law competitions or AP exams, there definitely wasn't any extra time for procrastinating. The key for me was learning how to do homework in small chunks-- at lunch, during our mandatory study hall, while sitting in splits at the gym, etc. I even lugged my violin to the gym and serenaded everyone during snack break before important orchestra events. If I could do one calc problem per pre-split stretch and then two while in splits (per leg), that ended up being 1/3 of my math homework. I also read while sitting in splits (answering questions about what I was reading was always fun, especially when we did The Inferno and The Decameron...). Also, my best friends were also involved in a lot of activities, so we would have a lot of study groups that met around 9 and finished between midnight and 1. My life was one of sleep deprivation, but everything worked out really well in the end. The only way I made it through high school was by learning how to break assignments into small chunks and to always stay on top of the work.
However, it was probably easier for me to balance school and gymnastics because I absolutely knew what my priority was: gymnastics was not going to get me into college; academics was. I was not in a position to compete NCAA, except maybe as a walk-on at the very weakest D1 schools, and my coaches were also realistic and let me miss the occasional practice or sit out a strong event if I had too much homework.