z-transformer

After seeing the Transformers movie, Little Z decided to make his own transformer.

For start, he wants to make only 2D transformer, that is made of steel parts, and joints that connect different parts.

The description of the transformer can be represented by a 2D matrix in the following form:
.aa0bb.
Where '.' represents a free space, the letters represent the steel parts (each letter represents the same part) and finally '0' (zero) represents a joint.

Each joint can move in 90 degrees increments. The transformer above can look transform to:
.aa0
...b
...b

or

...b
...b
.aa0

But the following transformer can not transform at all (because of the way the parts are connected)

0aa0
b..c
b..c
0dd0

Little Z wants to send the transformer to his friend, and wants to use the smallest box possible. So he wonders, what is the smallest (in terms of area) 2D box he can use, so that the whole transformer fits inside.