  Using Barnes-Wall lattices and 1-cocycles on finite groups of monomial
matrices, we give a procedure to construct tricosine spherical codes. This was
inspired by a 14-dimensional code which Ballinger, Cohn, Giansiracusa and
Morris discovered in studies of the universally optimal property. It has 64
vectors and cosines $-3/7, -1/7, 1/7$. We construct the {\it Optimism Code}, a
4-cosine spherical code with 256 unit vectors in 16-dimensions. The cosines are
$0, 1/4, -1/4, -1$. Its automorphism group has shape $2^{1+8}{\cdot}GL(4,2)$.
The Optimism Code contains a subcode related to the BCGM code. The Optimism
Code implies existence of a nonlinear binary code with parameters $(16,256,6)$,
a Nordstrom-Robinson code, and gives a context for determining its automorphism
group, which has form $2^4{:}Alt_7$.
