We construct via linkage an arithmetically Gorenstein irreducible 3-fold $X = X_{16} \bf{P}^7$, of degree 16, having Betti table of type [420]. For an artinian reduction $A_F$, the quadratic part of the ideal $F^\perp$ is the ideal of six points on a twisted cubic curve. We construct $X_{16}$ as an anticanonical divisor in the fourfold intersection of a cubic scroll and quadric.
The betti table is $\phantom{WWWW} \begin{matrix} &0&1&2&3&4\\ \text{total:}&1&6&10&6&1\\ \text{0:}&1&\text{.}&\text{.}&\text{.}&\text{.}\\ \text{1:}&\text{.}&4&2&\text{.}&\text{.}\\ \text{2:}&\text{.}&2&6&2&\text{.}\\ \text{3:}&\text{.}&\text{.}&2&4&\text{.}\\ \text{4:}&\text{.}&\text{.}&\text{.}&\text{.}&1\\ \end{matrix} $
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