The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 X 0 0 X 0 X X 2X 0 0 X X 2X 2X 2X 0 X 0 0 X 0 2X X 2X X 2X 0 X X 0 0 0 X 2X X 0 0 0 X 2X 2X 0 2X 2X 2X X 0 2X 0 X 2X 0 X generates a code of length 18 over Z3[X]/(X^2) who´s minimum homogenous weight is 33. Homogenous weight enumerator: w(x)=1x^0+36x^33+186x^36+18x^42+2x^54 The gray image is a linear code over GF(3) with n=54, k=5 and d=33. This code was found by Heurico 1.16 in 0.000957 seconds.