  In this paper, for an even integer $n\geq 4$ and any positive integer $k$
with ${\rm gcd}(n/2,k)={\rm gcd}(n/2-k,2k)=d$ being odd, a class of $p$-ary
codes $\mathcal{C}^k$ is defined and their weight distribution is completely
determined, where $p$ is an odd prime. As an application, a class of nonbinary
sequence families is constructed from these codes, and the correlation
distribution is also determined.
