What is the secret to the burnt treasure map with the Polytron logo, the candle room, and the floating black monolith?

After lowering the water level, there is a anticube room beneath the first warp zone. In New Game+ first-person view mode, the Polytron logo shows on the floor. After following the treasure map (standing exactly in the hole of the logo, entering the tetromino code on the reverse side), a floating black monolith/obelisk/pillar appears. What is the trick?

As discovered by a person on the Xbox360Achievements forum in this post, this puzzle can be solved just like the first puzzle in the same room. The following picture shows the floor of the room, which can be seen in first person view:

The first puzzle required a button input sequence while standing on the square with no line in it (circled in blue in the picture). This puzzle similarly requires standing on the square with a line in it (circled in green in the picture) and inputting the following button sequence.

down down LT RT RT A up

^{(To make the black monolith first appear, follow the burnt treasure map; or just stand atop the square on the left and enter ↑ RT ↑ A ↓ LT ↑ ↓.)}

Now, stand atop the square on the right and enter: ↓ ↓ LT RT RT A ↑

The black monolith turns into a heart piece (finally), thanks to gregSTORM.

Video:

gregSTORM used assisted brute force to discover this solution. It's still unclear how the puzzle was actually supposed to be solved. See "How is the Monolith puzzle in Fez supposed to be solved?" for links to some threads that discuss possibilities.