  We construct two series of linear codes over finite ring
$\mathbb{F}_{q}[x]/(x^2)$ and Galois ring $GR(p^2,m)$ respectively reaching the
Griesmer bound. They derive two series of codes over finite field
$\mathbb{F}_{q}$ by Gray map. The first series of codes over $\mathbb{F}_{q}$
derived from $\mathbb{F}_{q}[x]/(x^2)$ are linear and also reach the Griesmer
bound in some cases. Many of linear codes over finite field we constructed have
two Hamming (non-zero) weights.
