The generator matrix 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 X 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 X 1 X 1 2X 2X 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 2X 1 X 1 1 0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 2X+1 1 2 0 2 1 2X+1 0 2 2X+1 X 1 X+2 2X+1 0 1 2X 1 2X+1 1 0 1 1 2X X+2 2X+2 X+2 2X+1 X 2X+1 2X+2 X+1 2X+1 1 X X 1 1 X+1 X+1 2 2X+1 2 X+2 1 1 X 2 0 0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 X 2X X 0 2X 0 2X X 2X 0 0 X X 0 0 X 2X X X 2X 0 2X 0 2X 2X 2X 0 X X X 0 2X 0 0 0 2X 0 2X X X 2X 0 2X X 0 2X 2X 2X X 0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X X 2X 2X X X X 2X 0 X X 0 X 0 X X X 2X X 0 2X 2X X 2X 0 0 0 2X 2X 2X 0 2X X 2X 0 0 2X 2X 2X X 0 X 2X 2X 0 2X X 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X X 2X 2X X 2X X 2X X X 2X 2X X 0 X X 2X X X 0 X 0 X 0 0 X 2X 2X 0 X 2X 2X 0 X 2X 0 X X 0 X X 2X 0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X X 2X 2X X 0 0 0 2X X 0 2X 0 X 0 2X 2X 2X 2X 2X 0 2X X X X X 0 X X X 2X X X 2X 0 2X 0 2X 0 X X 2X 0 2X 2X 0 2X 0 X 2X 0 0 0 0 0 0 X 0 X 0 X X X 2X 2X X X 0 0 X 0 2X 2X X 2X X 0 0 0 X 0 0 X X 2X 0 0 X 0 X 0 2X 0 0 2X 2X 2X X X X X 2X 0 2X 2X X 0 X X 0 0 X 2X X 0 0 0 0 0 0 0 0 X X X X 0 2X X 2X 0 2X 2X 0 0 X 2X 2X 2X 0 X 2X 2X X 2X 2X 0 0 2X X X 2X X 0 0 0 X 0 2X 0 X X 0 0 X 0 0 2X 0 X 2X 2X 0 X X 0 2X X 2X X generates a code of length 65 over Z3[X]/(X^2) who´s minimum homogenous weight is 108. Homogenous weight enumerator: w(x)=1x^0+104x^108+6x^110+270x^111+120x^113+460x^114+702x^116+756x^117+1560x^119+1156x^120+2880x^122+1794x^123+5154x^125+2546x^126+7170x^128+3000x^129+8322x^131+3336x^132+6810x^134+2602x^135+4014x^137+1598x^138+1938x^140+916x^141+618x^143+532x^144+48x^146+304x^147+24x^149+178x^150+68x^153+40x^156+10x^159+6x^162+2x^165+2x^168+2x^174 The gray image is a linear code over GF(3) with n=195, k=10 and d=108. This code was found by Heurico 1.16 in 56.6 seconds.