  We present a reflexive Banach space with an unconditional basis which is
quasi-minimal and tight by range, i.e. of type (4) in Ferenczi-Rosendal list
within the framework of Gowers' classification program of Banach spaces, but
contrary to the recently constructed space of type (4) also tight with
constants, thus essentially extending the list of known examples in Gowers
classification program. The space is defined on the base on a boundedly
modified mixed Tsirelson space with use of a special coding function.
