Let A be a unitary ring with an involution ∗. The groups SL ∗ ( 2 , A ) , defined by Pantoja and Soto-Andrade in [J. Pantoja, J. Soto-Andrade, A Bruhat decomposition of the group SL ∗ ( 2 , A ) , J. Algebra 262 (2003) 401–412], are a non-commutative version of the special linear groups SL ( 2 , F ) defined over a field F . Soto-Andrade, in [J. Soto-Andrade, Représentations de certains groupes symplectiques finis, Bull. Soc. Math. France Mém. 55–56 (1978)], using this approach gave a new presentation of the symplectic group Sp ( 2 n , F q ) and used it to construct Weil representations of this group. In this paper, we classify the involutions of A m = F q [ x ] / 〈 x m 〉 and we study the groups SL ∗ ( 2 , A m ) . We give a presentation of these groups as in [J. Pantoja, A presentation of the group SL ∗ ( 2 , A ) , A a simple artinian ring with involution, Manuscripta Math. 121 (2006) 97–104] and finally, we construct a Weil representation of SL ∗ ( 2 , A m ) following the line of thought given in [J. Soto-Andrade, Représentations de certains groupes symplectiques finis, Bull. Soc. Math. France Mém. 55–56 (1978)].