visual - Wooden Snake Puzzle

I have a wooden snake puzzle in my collection that has been unsolved for years. I wondered if any of you might be interested. I have fiddled with it, but think it might need dynamic programming or something to solve. But maybe some of you have an approach that would work.

The puzzle is pictured below. It consists of 64 wooden cubes each of which (except the ends) has a hole in the center of two of the faces. An elastic is threaded through the whole thing so that the pieces can swivel in place. The objective is to arrange it into a 4x4x4 cube.

So, for example, starting at the bottom end (in the picture), there are 3 in a row. The last of these three has the fourth cube coming off at right angles. The direction it comes off can be swivelled, and that entire next segment (also 3 in a row: blocks 4-6) can swivel around so that it doubles back on itself, or sticks out at right angle or continues straight with a kink.

The last of these is impossible, of course, because the length would be 5 and therefore it would not fit into a 4x4x4 cube.

Here is a description of the entire snake:

3 - 2 - 3 - 2 - 2 - 4 - 2 - 3 - 2 - 3 - 2 - 3 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 3 - 3 - 2 - 2 - 2 - 2 - 2 - 3 - 4 - 2 - 2 - 2 - 4 - 2 - 3 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 4 - 2

In the above sequence, each corner is counted twice. There are 46 segments, so 45 corners, which is why the above numbers sum to 109 rather than 64. Hopefully that makes sense.

Would love to hear your thoughts. Even partial insights would be helpful.

Enjoy!

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Thanks to @Jaap Scherphuis, it is now neatly solved! Me: >10 years without success. The internet: <1h. Gotta love it.

Answer

I have the same snake cube puzzle, except that its cubes don't alternate in colour. On mine they are coloured so that the finished cube consists of 2x2x2 blocks.

Drawing of the solution is under the spoiler:

The 3x3x3 version of this puzzle is very common, though almost all versions use the same configuration of straight and bent cubes. You can find out more about these smaller versions on my snake cube page.