In most programs, black type always overprints colored objects behind it. If you ever want the type to not overprint, create a new color defined as 99% black and use it for your type. Your text will still print totally black, but you can assign this color any trapping value you’d like.
In QuarkXPress, choose Edit> Colors… and click the New button (or click the + symbol on the Colors palette) and make changes similar to this:
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