The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X X X X X 0 0 0 0 X 0 X 0 X 2X 2X 2X 0 0 X X 0 X 2X 2X 2X 0 0 X X 0 X X X 2X 2X X 2X X X X 0 0 X 2X 2X X 0 X 2X 0 X 2X X 2X 0 0 X 2X 0 X 2X X 2X 2X 0 X 0 X 0 2X 0 X 2X generates a code of length 33 over Z3[X]/(X^2) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+72x^66+6x^72+2x^81 The gray image is a linear code over GF(3) with n=99, k=4 and d=66. As d=66 is an upper bound for linear (99,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4. This code was found by Heurico 1.16 in 0.00392 seconds.