  Let $K$ be an imaginary quadratic field. Modular forms for GL(2) over $K$ are
known as Bianchi modular forms. Standard modularity conjectures assert that
every weight 2 rational Bianchi newform has either an associated elliptic curve
over $K$ or an associated abelian surface with quaternionic multiplication over
$K$. We give explicit evidence in the way of examples to support this
conjecture in the latter case. Furthermore, the quaternionic surfaces given
correspond to genuine Bianchi newforms, which answers a question posed by J.
Cremona as to whether this phenomenon can happen.
