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In this paper, we study constacyclic codes of length n = 7 p s over a finite field of characteristics p , where p ≠ 7 is an odd prime number and s a positive integer. The previous methods in the literature that were used to compute the Hamming distances of repeated-root constacyclic codes of lengths n p s with 1 ≤ n ≤ 6 cannot be applied to completely determine the Hamming distances of those with n = 7. This is due to the high computational complexity involved and the large number of unexpected intermediate results that arise during the computation. To overcome this challenge, we propose a computer-assisted method for determining the Hamming distances of simple-root constacyclic codes of length 7, and then utilize it to derive the Hamming distances of the repeated-root constacyclic codes of length 7 p s. Our method is not only straightforward to implement but also efficient, making it applicable to these codes with larger values of n as well. In addition, all self-orthogonal, dual-containing, self-dual, MDS and AMDS codes among them will also be characterized. [ABSTRACT FROM AUTHOR]