  We provide an explicit presentation of an infinite hyperbolic Kazhdan group
with $4$ generators and $16$ relators of length at most $73$. That group acts
properly and cocompactly on a hyperbolic triangle building of type $(3,4,4)$.
We also point out a variation of the construction that yields examples of
lattices in $\tilde A_2$-buildings admitting non-Desarguesian residues of
arbitrary prime power order.
