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Coherent propagation of supermodes in a multicore fiber is promising for power scaling of fiber laser systems, eliminating the need for the active feedback system to maintain the phases between the channels. We studied the propagation of broadband pulsed radiation at a central wavelength of 1030 nm in a multicore fiber with coupled cores arranged in a square array. We designed and fabricated a silica multicore fiber with a 5 × 5 array of cores. For controllable excitation of a desired supermode, we developed a beam-forming system based on a spatial light modulator. We experimentally measured intensity and phase distributions of the supermodes, in particular, the in-phase and out-of-phase supermodes, which matched well the numerically calculated profiles. We obtained selective excitation and coherent propagation of broadband radiation with the content of the out-of-phase supermode of up to 90% maintained without active feedback. Using three-dimensional numerical modeling with allowance for a refractive index profile similar to those of the developed fiber, we demonstrated stable propagation of the out-of-phase supermode and collapse of the in-phase supermode at a high signal power.