Best tool for finding uncorrelated baskets of currency pairs?

I'm looking for a basket of 3-6 currency pairs to trade on the 1hr or 4hr timeframe, with the stipulation that they are all as uncorrelated with each other as possible.

What is the best tool or method for finding the most uncorrelated basket of 3-6 currencies on the 1hr and/or 4hr timeframe?

I don't have any restriction on the currency pair as long as the spread is normally under 10 pip

I am afraid that what you won't find a "neutral" basket of 6 with under 10 pips each. You have to lighten up one of your criteria (either the spread range, either the degree of correlation, either the amount of pairs. If I were you I'd be looking for a 2-sided basket:
Half of it slightly correlated to the dollar, half of it slightly correlated to the euro, and spreading the risk so that any big move on the Euro/Doll would have a neutral impact on your basket.
There has to be several ways of estimating the degree of correlation in between pairs, but it is never 0 when it gets to Majors, and it is a dynamic: it evolves along with time