Varieties of small degree with respect to codimension and ample vector bundles

Let E be an ample vector bundle on a projective manifold X, with a section vanishing on a smooth subvariety of the expected dimension, and let H be an ample line bundle on X inducing a very ample line bundle H_Z on Z. Triplets (X,E,H) as above are classified assuming that Z, embedded by |H_Z|, is a variety of small degree with respect to codimension