The generator matrix 1 0 0 1 1 1 1 1 1 2X 0 1 X 1 1 1 1 1 1 X 1 1 X 1 1 1 X 1 X 1 1 X 1 0 1 1 1 1 1 2X X 1 1 0 1 1 2X 1 1 2X 1 1 1 1 2X 2X 2X 1 1 2X 1 1 1 0 1 0 0 X 2X+1 1 2 2X+1 1 1 2 2X 2X+1 1 1 X+2 2X+2 X 1 X 2X+2 1 1 0 X+2 1 1 0 0 2X+1 1 2 1 2X+2 X+1 2X+1 2X 2X+2 1 X X X+2 1 X X+1 1 2X+1 2X 1 0 1 X 2X 1 1 1 0 X+1 X 2X X 2X 0 0 1 1 2X+2 X+2 X+1 0 2X 2X+1 2X+2 X 1 2 1 2X 2X+1 2 X 0 X+2 X+1 X+2 1 X+1 2X+2 2X+1 X+2 1 2X+1 1 X+2 2 X X 2X+1 X+2 2X+1 2X X 1 0 2X+2 0 2X 2X+2 2X+2 1 2X 2X X+2 2 X 2X+1 X 2X 2X+2 2X X+1 1 2X+2 X+2 1 0 0 0 2X 2X 2X 2X 2X X 2X 2X X 2X 0 X 0 X 2X 2X 2X 0 2X 0 0 0 X 0 X X 2X 0 2X X 0 0 2X 0 X X 2X X 2X 2X X X X X X 0 0 2X X X 0 X 2X 0 0 0 0 X 2X 0 generates a code of length 63 over Z3[X]/(X^2) who´s minimum homogenous weight is 119. Homogenous weight enumerator: w(x)=1x^0+210x^119+172x^120+474x^122+194x^123+204x^125+88x^126+192x^128+118x^129+174x^131+90x^132+72x^134+26x^135+60x^137+14x^138+54x^140+20x^141+12x^143+2x^144+6x^146+2x^150+2x^156 The gray image is a linear code over GF(3) with n=189, k=7 and d=119. This code was found by Heurico 1.16 in 0.136 seconds.