In 'Computational Experience with Lenstra's Algorithm' by L Gao, Y Zhang it is claimed that they have an implementation of Lenstra's fixed dimension integer programming algorithm. Is this available online anywhere?
Is Barvinok's algorithm available online?
This may be of some help:
De Loera, Jesús A., David Haws, Raymond Hemmecke, Peter Huggins, and Ruriko Yoshida. "A computational study of integer programming algorithms based on Barvinok's rational functions." Discrete Optimization 2, no. 2 (2005): 135-144. (Elsevier link.)