  We study a sixth order derivative scalar field model in Minkowski spacetime
as a toy model of higher-derivative critical gravity theories. This model is
consistently quantized when using the Becchi-Rouet-Stora-Tyutin (BRST)
quantization scheme even though it does not show gauge symmetry manifestly.
Imposing a BRST quartet generated by two scalars and ghosts, there remains a
non-trivial subspace with positive norm. This might be interpreted as a
Minkowskian dual version of the unitary truncation in the logarithmic conformal
field theory.
