Optical fibers provide a favorable medium for nonlinear optical processes owing to the small mode field size and concurrently high optical intensity combined with the extended interaction lengths. Second harmonic generation (SHG) is one of those processes that has been demonstrated in silica glass optical fibers. Since silica is centrosymmetric, generating SHG in an optical fiber requires poling of the glass. In addition and when one wants to use ultrashort pulses for SHG, achieving both phase and group velocity matching is crucial. Although fibers that feature either modal phase velocity or group velocity matching for SHG have been reported, the possibility of simultaneous modal phase and group velocity matching was never reported before. In this paper we address this challenge, and for the first time to our knowledge, we show that it is feasible to do so with silica microstructured optical fibers featuring at least one ring of air holes in the cladding and a heavily Germanium doped core (above 25 mol.%) by exploiting the LP₀₁(ω) and LP₀₂(2ω) modes at 1.06 µm pump and 0.53 µm second harmonic wavelengths. This finding can greatly impact applications requiring waveguide based SHG generation with ultrashort pulses, including microscopy, material characterization and nonlinear imaging.