Certain Heusler phases belong to the materials which are discussed as potential half metals. Here, results of tunneling experiments with the full-Heusler alloy Co2Cr0.6Fe0.4AlCo2Cr0.6Fe0.4Al are presented. The Heusler alloy is used as an electrode of magnetic tunneling junctions. The junctions are deposited by magnetron DC sputtering using shadow mask techniques with AlOxAlOx as a barrier and cobalt as counter electrode. Measurements of the magnetoresistive differential conductivity in a temperature range between 4 and 300 K are shown. An analysis of the barrier properties applying the Simmons model to the bias dependent junction conductivity is performed. VSM measurements were carried out to examine the magnetic properties of the samples.