The generator matrix 1 0 0 1 1 1 1 1 0 2X 1 1 1 X 1 1 1 1 X 1 1 1 1 X 1 0 1 0 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 X 1 1 1 X 2X 1 1 1 1 X 2X X X 2X 1 0 1 0 1 0 2 1 2 1 1 0 2X+1 2X+2 1 X 2X+1 X 2X+1 0 0 2 1 2X+2 1 2X+2 1 2X X 2X+2 2X+2 2 1 1 X+2 0 X+1 X+1 2X 2X+1 0 X+1 2X+1 1 X+1 2X X 2X+2 0 2X 2 0 1 1 X+2 2X+2 X+1 0 1 1 1 0 X 0 0 0 1 2 1 2 1 0 2 2X+1 2 2X 2X+1 1 2X+2 2X+2 X+1 X 1 0 X X+1 2X+1 2X+2 X+2 X 2X+1 1 0 X+2 1 2X 2X+2 2X X 2X+1 X+2 1 2X+2 X+2 X+1 2X 2X X+1 1 X 1 1 0 X+2 0 2X+1 2 X+2 X 2X X X+1 X+2 2 1 1 0 0 0 0 2X 0 0 0 0 0 0 0 0 2X 0 0 X 2X X 2X 2X X 2X 2X 2X 2X 2X 0 2X 2X X X 2X 2X 2X 2X X 0 2X 0 0 2X 0 0 X X X X 2X 0 2X 0 2X 0 2X X X 0 2X 0 X 2X 0 0 0 0 0 0 2X 0 0 0 0 0 X 2X 0 0 2X X 2X 2X 0 X 2X X 0 X 2X 2X X X 2X X 0 2X 0 X 2X 2X X 0 X X 2X 0 X 0 0 2X X 2X 2X 2X X 0 2X X 0 2X 2X 2X 2X X 0 2X 2X 0 0 0 0 0 X 0 X X 2X X 2X 2X 0 X 2X 2X 2X 2X 2X 2X 2X X 0 X 2X 0 2X 0 2X 0 0 X 2X 2X 0 0 2X 0 2X 0 0 2X X 2X 0 2X X X 2X X 0 2X X 2X 2X 2X 2X 2X 0 X 2X 0 0 0 0 0 0 0 X X X X 0 0 2X 2X 0 0 X 0 X 0 X X 2X X X 2X 2X 0 2X X 2X 2X 0 X 0 X 2X 0 0 2X 0 2X 0 X X 0 0 0 X 2X 2X X 2X 0 X X 2X 0 0 X 2X X 2X generates a code of length 63 over Z3[X]/(X^2) who´s minimum homogenous weight is 108. Homogenous weight enumerator: w(x)=1x^0+72x^108+90x^109+78x^110+442x^111+618x^112+324x^113+900x^114+1236x^115+810x^116+1382x^117+2262x^118+1296x^119+2218x^120+3342x^121+1692x^122+2938x^123+4404x^124+2562x^125+3430x^126+4986x^127+2556x^128+3148x^129+4032x^130+1962x^131+2646x^132+3054x^133+1212x^134+1482x^135+1512x^136+498x^137+616x^138+534x^139+126x^140+186x^141+162x^142+6x^143+122x^144+6x^145+52x^147+6x^148+20x^150+18x^153+4x^156+6x^159 The gray image is a linear code over GF(3) with n=189, k=10 and d=108. This code was found by Heurico 1.16 in 47.2 seconds.