Let K be a field equipped with a valuation. Tropical varieties over K can
be defined with a theory of Gr\"obner bases taking into account the valuation
of K. Because of the use of the valuation, this theory is promising for
stable computations over polynomial rings over a p-adic fields.We design a
strategy to compute such tropical Gr\"obner bases by adapting the Matrix-F5
algorithm. Two variants of the Matrix-F5 algorithm, depending on how the
Macaulay matrices are built, are available to tropical computation with
respective modifications. The former is more numerically stable while the
latter is faster.Our study is performed both over any exact field with
valuation and some inexact fields like Q_p or F_q[[t]]. In the latter case, we track the loss in precision,
and show that the numerical stability can compare very favorably to the case of
classical Gr\"obner bases when the valuation is non-trivial. Numerical examples
are provided