Protoboard/Veroboard alternative for huge LED sign?
This is pretty close at 58cm wide, although only 10cm tall.

However, assuming board(s) will be mounted on something, why not use two (or more) pieces of veroboard? You could bolt/epoxy/solder some together.

Most PCB manufacturers can make you a board this size if that is an option.   

The 60cm sounds about right for 2.54mm pitch, but how do you calculate 360 holes needed for 114 LEDs? (are they 3 leads?)  

Things like a rough diagram of your intended setup, type of LEDs used, picture of VeeCAD layout might be helpful to find the best solution.