Four strips, side-by-side parallel and attached, will cover the top and half an adjacent face. Another such set of four will cover the bottom and half of another (or the same) adjacent face.

That leaves 12 successive unit squares on each of the four rows of the four adjacent squares on the sides. The remaining eight strips will cover these.

You can get fancier and place the initial four (and then the second four) by placing in pairs rather than four-abreast, overlapping opposite sides.  In that case, the remaining eight to be wrapped around the sides will not be touching end-to-end as only two groups of six in a row will be available on each of the four courses around the sides, interrupted by the width-2 overlaps from the top or bottom.