East German Command is a playable country in the game that is comprised of East germany, west-half of Poland, Czech region, Romania and Austria/Hungary. While small and not having much room for expansion, East German Command is one of the most influential factions that can decide the outcome of the war.
As said earlier you have little room for expansion. East German Command should play a supporting role to its bigger brother West German Command. As West German Command blitzs West, you should follow up by taking and securing Denmark, as well as Belgium/Netherlands. Sending a few Construction SCVs to France and building some bunkers should hurry France along to capitulate relatively quickly.
In the middle-game you need to build up your economy. 12 minutes is not a lot of time to prepare for Operation Barabossa. You wouldn't produce the Science you need to have Panther V tanks in time, it is highly recommended that you instead go for Advanced AT guns and send leftover Science to West German Command. Advanced AT guns with some supporting infantry will provide a strong backbone to the tank horde that the Soviets will send at you.
Build as many defences on the border with the Soviets as you are able including tank traps and AT bunkers. Support the West German advance as much as you can being careful not to overextend as your units would be slower and easily caught. Focus on finding the unit production facilities and destroying it. You may need to push up into Siberia to find most of the economy there. Make sure to keep Denmark and North Germany defended from any sea-borne invasion. Nordic countries and the UK love to use Denmark as a landing zone, where they spam bunkers and attack Germany from behind.
Another strategy is to build up a small army in the Balkans and use it to invade Greece and/or Yugoslavia before they can bring their defences to bear. Doing so would give you a huge boost to the economy and, depending on how well they are capable at defending, wouldn't damage your army much with some smart unit choices. Using an effective force of tanks supported by artillery and infantry to punch through the defences and take the cities quickly before Operation Barabossa begins.