  In this paper, we give a parity check matrix for the $(+)$-extended twisted
generalized Reed Solomon (in short, ETGRS) code, and then not only prove that
it is MDS or NMDS, but also determine the weight distribution. Especially,
based on Schur method, we show that the $(+)$-ETGRS code is not GRS or EGRS.
Furthermore, we present a sufficient and necessary condition for any punctured
code of the $(+)$-ETGRS code to be self-orthogonal, and then construct several
classes of self-dual $(+)$-TGRS codes and almost self-dual $(+)$-ETGRS codes.
