The walnut roots will grow up into the soil of the raised beds, in order to access the oxygen of which they will have been deprived. A juglone sensitive plant such as tomato shouldn't be within 50 or so feet of the drip line. ;-(

Here is a link that might be useful: Juglone facts

You have received good advice. Let me add that there is some evidence that juglon leaches from the air, especially after a rain. And the buds of the black walnut tree are second only to the roots in the amount of toxicity. Juglon is NOT water soluable. More water does not dilute the toxin. For something as sensitive as tomato plants I would get at least 75 feet away. Fifty feet, though may suffice.

It is interesting how many of these "fact sheets" vary in their information. I once saw a list of toxic sensitive and toxic tolerant plants. The Norway Spruce was on BOTH lists.
It is a crap shoot for sure.

Barbara aka Hawkeye Belle

I agree - don't waste your time w/ raised beds.
At our old house, our neighbor had 3 very tall 100 year old BW trees on the other side of her yard - her 2 story house was between the trees & our yard. For 15 years I couldn't figure out why certain plants could grow on the right side of our yard, but couldn't grow on the left side - same conditions.
Juglone travels!

I should also mention that ALL parts of black walnut (and other plants in the same family) affect other plants with the chemicals that are in fallen leaves and even rainwater dripping from their branches. So, it's not just the roots that you need to consider.