Usually you would want the roots planted lower to keep them from drying out. I haven't heard of problems with raised bed but roots should not be close to ground surface. Give your plants a few years to establish better roots without harvesting spears. Then harvest in increasing periods each year: 2,4,6 8 weeks. Since you planted seeds you'll not have benefits of male hybrid spear size but flavor should be same. Apply high Nitrogen fertilizer in spring and again after you stop harvesting; again in increasing increments. Grass can be controlled by saltwater sprinkle since asp. tolerates much salt.

Thanks for the advice. My neighbour has been growing his Asparagus in raised beds for well over a decade and he doesn't seem to have any troubles. Plus, my raised little bed that I built is more of a.... well, a bed surrounded by 2X4's rather than a raised bed (in the traditional sense).

Male asparagus plants produce more spears than females. I put compost on my bed in the fall and I put a nice layer of shredded leaves over that. I rarely have any weeds in my asparagus.

My only tip is that once your asparagus develops (at least two years) you can NEVER get rid of it. It's impossible to dig up and destroy. It will keep coming back year after year. Just be sure it's where you want it.