On the divisor class group of double solids

For a double solid V --> P-3 branched over a surface B subset of P-3 (C) with only ordinary nodes as singularities, we give a set of generators of the divisor class group Pic ((V) over tilde) congruent to H-2((V) over tilde, Z) in terms of contact surfaces of B with only superisolated singularities in the nodes of B. As an application we give a condition when H*((V) over tilde, Z) has no 2-torsion. All possible cases are listed if B is a quartic. Furthermore we give a new lower bound for the dimension of the code of B.