  One of the main goals of coding theory is to construct codes with best
possible parameters and properties. A special class of codes called
quasi-twisted (QT) codes is well-known to produce codes with good parameters.
Most of the work on QT codes has been over the 1-generator case. In this work,
we focus on 2-generator QT codes and generalize the ASR algorithm that has been
very effective to produce new linear codes from 1-generator QT codes. Moreover,
we also generalize a recent algorithm to test equivalence of cyclic codes to
constacyclic codes. This algorithm makes the ASR search even more effective. As
a result of implementing our algorithm, we have found 103 QT codes that are new
among the class of QT codes. Additionally, most of these codes possess the
following additional properties: a) they have the same parameters as best known
linear codes, and b) many of the have additional desired properties such as
being LCD and dual-containing. Further, we have also found a binary 2-generator
QT code that is new (record breaking) among all binary linear codes and its
extension yields another record breaking binary linear code.
