Representation of the pieces
----------------------------

Okay, after changing the scanning code, the bits mean the following:

7012
6543

and we rotate about 0.

Piece 76543210
  O1  00110011
  O2  11100001
  S   10110001
  Z   01100011
  L   11000011
  J   10010011
  I   10000111
  T   10100011

Apart from the right-hand column which is all 1, there's no obvious way to make these overlap, so let's use a long. The order of the pieces is hardly constrained, a sure sign we can do better:

O1 0011001-
S        1011000-
Z              0110001-
L                    1100001-
J                          1001001-
I                                1000011-
T                                      1010001-
   00110010110001100011000010010010000110100010
Hex   3   2   C   6   3   0   9   2   1   A   2

I can't see a way to make the leading digit 0. That'll do for now.