An \([n,k,d]\) linear \(q\)-code \(C\) is NMDS if both \(C\) and \(C^\bot \) have the Singleton defect equal to \(1\). The paper is concerned with classification of NMDS when \(q = 7,8,9\) and \(k=3\). Every \([n,3,n-3]\) NMDS code is equivalent to a set of \(n\) points in \(\text{PG}(2,q)\) no four of which lie on a line, while the set contains at least one collinear triple. The authors describe an algorithm (which is a modification of their earlier algorithm) that has been used to perform a search for such sets. The results are reported in form of tables giving the number of nonequivalent NMDS codes, for each \(n\) and \(q\). The maximal \(n\) for which NMDS codes exist are equal to \(15\) if \(q = 7,8\), and to equal \(17\) if \(q=9\).