The generator matrix 1 0 0 1 1 1 1 1 1 2X 1 1 1 1 2X X 1 1 1 X 2X 1 1 0 1 1 1 2X 0 1 1 1 1 1 1 1 2X 0 1 1 1 1 X 2X 1 0 1 1 0 1 1 1 X 1 1 1 2X 2X 1 1 1 0 X 0 1 0 2X 1 2X+1 2 0 X+2 1 2X+2 2X+1 X+1 X+2 1 1 2X+2 X X+2 1 1 X 1 2X X+1 2X 2 X 1 X+2 X 2X 2X+2 X+1 2X+1 0 0 1 X+1 2 X+1 0 1 1 2X+2 1 X+2 2X X X+1 1 X 1 1 2X+1 0 2X 1 0 X 2X+1 1 1 0 0 1 2X+1 1 2X 2X+2 2 X 1 X+2 2 X+1 2X+1 2X+2 X 2 1 X+1 0 2X+1 0 X 1 2 2X X 1 2 2X+2 2X+2 2X+2 0 2X+1 1 2X 1 X+2 2X X+1 X X+2 1 X+2 2X+1 X 0 1 1 X+2 X+2 X+1 2X 2 X+2 X+1 1 X 1 2X+1 2X+2 2X+2 2X+2 generates a code of length 63 over Z3[X]/(X^2) who´s minimum homogenous weight is 123. Homogenous weight enumerator: w(x)=1x^0+342x^123+226x^126+54x^129+60x^132+12x^135+30x^141+4x^144 The gray image is a linear code over GF(3) with n=189, k=6 and d=123. This code was found by Heurico 1.16 in 3.87 seconds.