<image>Below is a histogram depicting the number of hits on the same target by a certain artillery company over 8 weeks during new recruit training:

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$(1)$ Calculate the total hit frequency $p_{0}$ over these 8 weeks for the artillery company, and determine in which week the hit frequency was the highest;
$(2)$ Using $p_{0}$ from $(1)$ as the hit rate for artilleryman A of the company on the same target, if each shot is independent and artilleryman A fires 3 times, let $X$ be the number of hits. Find the mathematical expectation of $X$;
$(3)$ Using $p_{0}$ from $(1)$ as the hit rate for the artilleryman of the company on the same target, find out how many such shells must be fired simultaneously at the target to ensure that the probability of hitting the target exceeds $0.99$? (Given $\lg 0.4=-0.398$).