13×13 {-1, +1} matrix of maximal determinant

Ratio of |Det R| to Barba bound: 1

M=R^TR=R R^T:

13  1  1  1  1  1  1  1  1  1  1  1  1
 1 13  1  1  1  1  1  1  1  1  1  1  1
 1  1 13  1  1  1  1  1  1  1  1  1  1
 1  1  1 13  1  1  1  1  1  1  1  1  1
 1  1  1  1 13  1  1  1  1  1  1  1  1
 1  1  1  1  1 13  1  1  1  1  1  1  1
 1  1  1  1  1  1 13  1  1  1  1  1  1
 1  1  1  1  1  1  1 13  1  1  1  1  1
 1  1  1  1  1  1  1  1 13  1  1  1  1
 1  1  1  1  1  1  1  1  1 13  1  1  1
 1  1  1  1  1  1  1  1  1  1 13  1  1
 1  1  1  1  1  1  1  1  1  1  1 13  1
 1  1  1  1  1  1  1  1  1  1  1  1 13

R:

+++++-+++--+-
-+++++-+++--+
+-+++++-+++--
-+-+++++-+++-
--+-+++++-+++
+--+-+++++-++
++--+-+++++-+
+++--+-+++++-
-+++--+-+++++
+-+++--+-++++
++-+++--+-+++
+++-+++--+-++
++++-+++--+-+

Notes:

1. Found by Raghavarao [R].
2. Circulant.
3. R unique up to equivalence [CD].