LOL the subject states 128 or and I quote "A little higher".
First off what power supply are you using as the required SEPARATE supply for the LED's as they do draw a good amount of current and its probably too much for an Arduino on its own.
The better strips from EBAY etc have a pair of seperate take off leads as well as the connector.
If yours has those USE THEM.
There are a multitude of sketches and libs for the "neopixel" type LED's But as the instructable states memory might be an issue. Might be worth playing with some of the other examples that are out there too as you might get better results.
There are a few ways to overcome that. Better Arduino, Store arrays on SD card readers, Read datas from a PC. Choice is yours depending on the path you want to take.
Also suggest you read the COMMENTS in that IS tutorial too as there are some good clues in there as to why you may not be getting the result you want....EG SHARED GROUND.
Seems the limit is already set anyway here
uint32_t last_update = 0;
uint8_t NUM_RGB = 128;
A better method to do what you need is here..