  Let $f$ be an holomorphic endomorphism of $\mathbb{C}\mathbb{P}^k$. We
construct by using coding techniques a class of ergodic measures as limits of
non-uniform probability measures on preimages of points. We show that they have
large metric entropy, close to $\log d^k$. We establish for them strong
stochastic properties and prove the positivity of their Lyapunov exponents.
Since they have large entropy, those measures are supported in the support of
the maximal entropy measure of $f$. They in particular provide lower bounds for
the Hausdorff dimension of the Julia set.
