Brother multifunction devices do not support TLS / SSL connections.
As grawity suggested, you can use stunnel. It ensures that email credentials as well as the content of your message are encrypted at least up to and within Google's platform. Here's our stunnel.conf:
accept = 0.0.0.0:25
connect = smtp.gmail.com:465
This instructs stunnel to accept incoming connections on port TCP 25 and forward them through an SSL tunnel to Google's SMTP servers on port TCP 465. The 0.0.0.0 is shorthand notation for all avialable IPv4 interfaces. 'client=yes' tells stunnel to operate as an SSL client rather than a server.
Be sure to open a pinhole on your proxy machine's firewall for port 25. Then point your Brother multifunction printer to the address of the machine running stunnel.
If your Internet connection uses a static IP address (or is very stable), you can skip encryption and fallback to plain SMTP. Simply use aspmx.l.google.com as the SMTP server address with port TCP 25.
You'll have to add your gateway IP address to the Email Whitelist box in your Google Apps control panel. Finally, if you have an SPF record for your domain, you'll need to adjust it accordingly to include your gateway IP address as a legitimate sender:
v=spf1 ip4:18.104.22.168 include:_spf.google.com ~all
If you don't know your gateway IP address, check dnsstuff.com (listed in the upper left hand corner).