An stratification of $B^4(2,K_C)$ over a general curve

For a general curve C of genus $g\ge 10$, we show that the Brill- Noether locus $B^4(2,K_C)$ contains irreducible sub-varieties $B_3\supset B_4 \supset \cdots \supset B_n$,where$B_n$isofdimension$3g-10-n$and$B_3$ is an irreducible component of the expected dimension $3g-13$.