Inspecting the upper part in search of any clues concerning the "story" for the (supposed) code, it is first and foremost the two face-like shapes that could grasp our attention:
Let's concentrate on the left one first and try to find out, what it could symbolize:
Examining the shape carefully, we may have the idea that it might be a (really clever) diagram of the Solar System we are looking at (the small signs are the astronomical symbols of the planets):
Let's collect the arguments that support this hypothesis:
- there are exactly 4 inner planets on the diagram, just like in the Solar System (Mercury, Venus, Earth, Mars);
- it is exactly the 3rd planet (the Earth), that is marked (by a triplet) on the diagram;
- there are 6 planets drawn separately, exactly the number of planets recognizable with naked eye (and known to each civilization).
Note: In 2001 (at the time of solving the code) there was also a fourth reason to mention: there are exactly 9 planets on the diagram, just like in the Solar System. Since 2006 Pluto is not counted as a planet anymore, and so this argument does not hold now. But it is not completely impossible to find a Planet X beyond Neptune, which of course would make the correspondence perfect.
To me it seems too much of a coincidence having this level of conformity, and, considering the other elements of the code as well (see further steps), that also indicate a high intelligence behind the design (in fact probably an even higher than we humans have today), I think this explanation could be the most plausible one.
Note: as far as I know, the official science for Mayan culture has no real interpretation for the distinct features of this figure, especially not in such detail.
If we accept the left figure as a representation of our solar system, then it is of course logical to discover a picture of another solar system in the shape on the right side:
This solar system seems to have three inner and three outer planets, and obviously there is no need to mark any of the planets or to differentiate between perceptible and hidden ones here.
Note: we could also pay some attention to the contrasting expressions of the two faces (the left one seems to be much younger and more vigorous), but it would be almost impossible to guess exactly what this dissimilarity could refer to, and it has no real relevance to solving the code either.
And finally, the bird at the top of the drawing, with the other system at its tail and our solar system at its head, could easily be interpreted as a symbol of an interstellar travel from the other system to the Earth:
So, we have a story now as a framework for exploring the code supposedly hidden in the arrangement of the triplets. The main question is, of course: where is the other system located, which solar system served as the starting point for this travel? Our intuition is that the triplets will give us a way to find the answer to this question, that they will help us identify the other system somehow.