Apportion the Blame

[rod]

My partner and I bid this poorly in a recent club game.

Matchpoints, red vs. white.

♠ AK985
♥ Q862
♦ 74
♣ QJ

1♠
2♥
3♦
5♦ **
Pass

♠ Q
♥ J75
♦ AKQ9862
♣ A5

2♦
3♣ *
4NT
6♦

* Fourth suit, artificial game force
** 1 or 4 key cards

This is a terrible contract. What do you think was the worst bid? How would you and your partner bid it?

By the way this actually made when a club was led and covered by the King.