  Linear codes are the most important family of codes in cryptography and
coding theory. Some codes have only a few weights and are widely used in many
areas, such as authentication codes, secret sharing schemes and strongly
regular graphs. By setting $ p\equiv 1 \pmod 4 $, we construct an infinite
family of linear codes using two distinct weakly regular unbalanced (and
balanced) plateaued functions with index $ (p-1)/2 $. Their weight
distributions are completely determined by applying exponential sums and Walsh
transform. As a result, most of our constructed codes have a few nonzero
weights and are minimal.
