How can I control a "high" voltage charlieplexed LED array?
You could use comparators such as LP339 and transistors (such as prebiased types) to buffer and level-translate  tri-state GPIOs.
Eg:



simulate this circuit &ndash; Schematic created using CircuitLab
For 14 pins it would require 7 dual prebiased transistors, 4 LP339 chips and 4 quad resistor packs, plus some dividers  to get the +1/+1.5/+2 voltages. You can use an op-amp to buffer the 1.5V.
However trying to Charlieplex 144 LEDs with 10mA is probably a very bad idea if you expect to illuminate a large number of them such that they appear to be on continuously. That's only 70uA average per LED which is very little current, even for a good LED. To get mA of average current means that  you'll exceed the maximum peak current rating of most small LEDs, which will affect reliability and lifetime.
I suggest you do some experimentation to determine what average current is acceptable before settling on an approach.