Construction of some unimodular lattices with long shadow
  In this paper, we construct odd unimodular lattices in dimensions n=36,37 having minimum norm 3 and 4s=n-16, where s is the minimum norm of the shadow. We also construct odd unimodular lattices in dimensions n=41,43,44 having minimum norm 4 and 4s=n-24. 
Masaaki Harada
math.CO math.NT