Try this in Julia for some extra speed:

    best = 0
    i = 0
    while true
        i += 1
        count = 0
        face = 1
        while face == 1
            face = rand(0:1)
            count += face
        end
        if count > best
            best = count
            println("new record: $best in iteration $i")
        end
    end

I wrote a short c program and ran it on 4 cores. Current best result is 36.