Generic ring for perfect modules of codimension 2

In recent years, there has been renewed interest in the topic with the description of generic rings for resolutions of length 3 by Jerzy Weyman. The interest then turned into analyzing the structure of perfect ideals of codimension 3. However, a case of perfect modules of codimension 2 was left out. In this note, we fill this gap by constructing a generic ring for perfect modules of codimension 2.