  One of the fundamental results in quantum foundations is the Kochen-Specker
no-go theorem. For the quantum theory, the no-go theorem excludes the
possibility of a class of hidden variable models where value attribution is
context independent. Recently, the notion of contextuality has been generalized
for different operational procedures and it has been shown that preparation
contextuality of mixed quantum states can be a useful resource in an
information-processing task called parity-oblivious multiplexing. Here, we
introduce a new class of information processing tasks, namely d-level parity
oblivious random access codes and obtain bounds on the success probabilities of
performing such tasks in any preparation noncontextual theory. These bounds
constitute noncontextuality inequalities for any value of d. For d=3, using a
set of mutually asymmetric biased bases we show that the corresponding
noncontextual bound is violated by quantum theory. We also show quantum
violation of the inequalities for some other higher values of d. This reveals
operational usefulness of preparation contextuality of higher level quantum
systems.
