2021 Update:
In 2021 no need for unique Id or being nfs, just list your synced folders:
config.vm.synced_folder ".", "/vagrant/Sites"
config.vm.synced_folder "../Code", "/vagrant/Code"
Original answer:
I just needed to set a unique ID for each mount, and then reload the vagrant box.
# Use NFS for the shared folder
config.vm.synced_folder ".", "/vagrant/Sites",
id: "sites", # <--- this ID must be unique
:nfs => true,
:mount_options => ['nolock,vers=3,udp,noatime']
# Use NFS for the shared folder
config.vm.synced_folder "../Code", "/vagrant/Code",
id: "code", # <--- different from this one
:nfs => true,
:mount_options => ['nolock,vers=3,udp,noatime']