I'm searching for a "simple" description of the basis of the Barnes-Wall lattices 
in (real) dimension $2^n$, if possible in a basis of minimal vectors, so that I can 
do some calculations.  
     
Can anyone tell me where to find such a description ?   

**Note :** I'm not looking for examples in fixed dimensions, like the D4, or E8 
lattices. I know where to look up those. I'm looking for a formula / systematic
description in all dimensions of powers of 2.