  We provide first explicite examples of quantum deformations of D=4 conformal
algebra with mass-like deformation parameters, in applications to quantum
gravity effects related with Planck mass. It is shown that one of the classical
$r$-matrices defined on the Borel subalgebra of $sl(4)$ with $o(4,2)$ reality
conditions describes the light-cone $\kappa$-deformation of D=4 Poincar\'{e}
algebra. We embed this deformation into the three-parameter family of
generalized $\kappa$-deformations, with $r$-matrices depending additionally on
the dilatation generator. Using the extended Jordanian twists framework we
describe these deformations in the form of noncocommutative Hopf algebra. We
describe also another four-parameter class of generalized
$\kappa$-deformations, which is obtained by continuous deformation of
distinguished $\kappa$-deformation of D=4 Weyl algebra, called here the
standard $\kappa$-deformation of Weyl algebra.
