<p>Low-Rank Parity check codes over finite fields have gained a lot of attention since their introduction in 2013 by Gaborit et al. as a new family of rank metric codes due to their application in cryptography particularly. After the definition of rank metric codes over finite principal ideal rings by Kamche et al., several works have generalized Low-Rank Parity check codes over finite commutative rings using notions in module theory. This rank metric is related to the number of elements in a minimal generating family of a module. Epelde et al. have introduced a new metric over Galois rings, taking into account the cardinality of the module and defined Gabidulin codes in this context. In this paper, we give the definition of Low-Rank Parity check codes with this new metric. We study some properties of the product of two submodule with the cardinal rank metric and derive the success probability of the decoder. We then compare this metric with the rank metric showing the advantages of the rank metric.</p>