  A homologically trivial part of any Turaev-Viro invariant odd order $r$ is a
Turaev-Viro type invariant order $\frac{r + 1}{2}$. In this paper we find an
explicit formulas for this Turaev -- Viro type invariant, corresponding to the
invariant order $r = 7$. Our formulas express $6j$-symbols and colour weights
in terms of $\gamma$, where $\gamma$ is a root of the polynomial
$\mathcal{T}(x) = x^3 - 2x^2 - x + 1$.
