i1 : R = QQ[a..c];
i2 : I = intersect(ideal(c-3*a,b-2*a),ideal(a-5*b,c+4*b));
i3 : G = flatten entries super basis(2,I);
i4 : B = flatten entries basis (2,R);
i5 : M = matrix apply(#G, i-> apply(#B, j -> coefficient(B_j,G_i)))
o5 = | 11 -19 9  0   0   0  |
     | 0  1   0  -19 9   0  |
     | 0  0   11 0   -19 9  |       
     | 0  0   0  12  -5  -2 |
i6 : flatten entries gens minors(4,M)
o6 = {15972, -6655, 27588, 1573, -25289, -2662, -13068, -4598, 18634, 10043, 2178, -11979, -6655, 11495, -5445}
i7 : gcd(oo)
o7 = 121
i8 : o6/o7
o8 = {132, -55, 228, 13, -209, -22, -108, -38, 154, 83, 18, -99, -55, 95, -45}

--Up to a common factor of 121, we see the same Plucker coordinates that 
appear as in our calculation by hand.  However, the order is different, 
due to Macaulay 2's use of a different ordering convention.