How can I fix my washer drain?

Hello. My washing machine drains directly before the tub drain in the adjecent bathroom (same line). I wish to filter the water exiting the washer with a trap, to prevent lint from entering the main sewer line, and reclogging. I was thinking of installing a utility tub, and extending the waher drain line with a trap to go into the tub, and then reconnecting the tub to drain to the original spot where the washer's drain tube is now connected. Does this sound feasible, and how much higher does the bottom of the tub need to be in relation to the high spot of the drain pipe it will be fitted to?