The generator matrix 1 1 1 1 1 1 0 X^2 0 0 X^2 0 0 0 X^2 0 2X^2 0 0 0 0 X^2 2X^2 0 generates a code of length 6 over Z3[X]/(X^3) who´s minimum homogenous weight is 6. Homogenous weight enumerator: w(x)=1x^0+12x^6+16x^9+666x^12+24x^15+10x^18 The gray image is a linear code over GF(3) with n=54, k=6 and d=18. This code was found by Heurico 1.16 in 0.000157 seconds.