How the heck do you solve that machine for the codes in 15 seconds? I’m losing codes trying.

Once you get the hang of it it’s not that hard for a beginner I understand but you need to understand the controls for how it works then it’s easier

Any tips?

I blew a whole card the first time I tried it too, the game does a very, very poor job of explaining it to you. I watched a youtube video first then went back to the game.
Firstly, try and ignore the timer, it's just a ticking clock that will stress you out. I am on PC, so I just use the arrow keys for the entire thing. When looking at the top code that you need to copy, divide it in half (horizontally). Use the left and right arrows to copy the top half and when that is done, use the down arrow to go to the next line then left and right to copy the bottom half. When done, hit enter to confirm (I think, from memory) and you will move to the next code fragment.
Once you get a couple done, you will get the hang of it. It's basically a game of Tetris Memory.
That's what worked for me anyway. I would recommend watching a youtube tutorial, so you get the general gist of it first and don't waste any more codes.

If you need to farm codes, unlock the Manhattan Bunker level first. Pretty short level and there are 3 officers in it to drop codes (well 3 after the first playthrough cause the uberkommadant drops a deathcard, but he is replaced with a regular officer once you kill him).

I usually memorize the code as soon as it appears, then focus only on the matching symbols. The biggest time-saver is planning your route before interacting with the machine.