1-4-4-4 is among the most awkward shapes when opening the bidding. The standard advice when I first started was to open 1♦ planning to rebid 2♣ if responder bid your singleton. This advice works well if opener is strong enough to complete his pattern. The partnership will find a game in any strain, if one exists, or play a reasonable partscore.
1♦ — 1♠
2♣ — 2♦
2♥ — ?
Opener’s Hand
♠ x
♥ AKxx
♦ AKxx
♣ KTxx