  Heterogeneous bipartite quantum pure states, composed of two subsystems with
a different number of levels, cannot have both reductions maximally mixed. In
this work, we demonstrate existence of a wide range of highly entangled states
of heterogeneous multipartite systems consisting of $N>2$ parties such that
every reduction to one and two parties is maximally mixed. Two constructions of
generating genuinely multipartite maximally entangled states of heterogeneous
systems for an arbitrary number of subsystems are presented. Such states are
related to quantum error correction codes over mixed alphabets and mixed
orthogonal arrays. Additionally, we show the advantages of considering
heterogeneous systems in practical implementations of multipartite steering.
