  Based on cyclic and consta-cyclic simplex codes, a new explicit construction
of a family of two-weight codes is presented. These two-weight codes obtained
are in the form of 2-generator quasi-cyclic, or quasi-twisted structure. Based
on this construction, new optimal binary quasi-cyclic [195, 8, 96], [210, 8,
104] and [240, 8, 120] codes, and good QC ternary [208, 6, 135] and [221, 6,
144] codes are thus obtained. It is also shown that many codes among the family
meet the Griesmer bound and thereful are optimal.
