There are a several things you need to address to get it working
@ouput
its @code
AddWithValue
since its not supposed to have a value just you Add
.ExecuteNonQuery
if you're not returning rows Try
SqlParameter output = new SqlParameter("@code", SqlDbType.Int);
output.Direction = ParameterDirection.Output;
cmd.Parameters.Add(output);
cmd.ExecuteNonQuery();
MessageBox.Show(output.Value.ToString());