A sum with constraints

Find the sum of all integers with at most 12 digits and containing exactly one '1', two '2', three '3' and four '4' in their digital representation (E.g: 23313447424)

You are given : 121970799987802920 (for all integers with at most 10 digits and containing exactly one '1', two '2' and three '3')

[My timing: 15 sec]