The generator matrix 1 0 1 1 1 1 1 2X^2+X 1 2X 1 1 1 1 0 1 1 2X^2+X 1 1 2X 1 1 1 1 1 2X 1 0 1 2X 1 1 1 2X^2+X 1 1 1 1 1 1 2X^2+X 1 2X^2+X 1 2X 1 1 1 1 0 1 0 1 X^2+X 1 1 X^2 1 2X^2+X 1 0 1 2X^2+2X+1 2 2X^2+X X+1 2X^2+X+2 1 2X^2+1 1 2X 2X+2 2 0 1 2X^2+2X+1 2X^2+X+2 1 X+1 2X^2+X 1 2X^2+1 2X 2X+2 2 2X^2+1 1 2X^2+2X+1 1 2X+2 1 0 2 2X+2 1 2X^2+X 0 2X^2+1 2 2X^2+2X+1 2X 1 2X+2 1 X^2+2X+2 1 2X^2+X 0 X^2+2X+2 X^2+2 1 2X^2+X 1 2X^2+2 1 2X^2+2X+1 X^2 1 X^2 1 0 0 0 2X^2 0 0 0 2X^2 2X^2 X^2 2X^2 2X^2 0 X^2 0 X^2 X^2 X^2 0 2X^2 X^2 2X^2 0 X^2 X^2 2X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 2X^2 X^2 X^2 0 0 X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 2X^2 X^2 2X^2 X^2 0 0 0 0 0 X^2 0 0 2X^2 2X^2 0 X^2 0 X^2 0 X^2 2X^2 2X^2 0 2X^2 0 X^2 X^2 2X^2 2X^2 X^2 2X^2 X^2 0 0 X^2 2X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 2X^2 X^2 2X^2 X^2 0 2X^2 X^2 2X^2 0 2X^2 0 X^2 2X^2 2X^2 0 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 0 0 0 0 0 2X^2 0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 0 0 0 2X^2 X^2 X^2 X^2 2X^2 X^2 X^2 X^2 X^2 2X^2 2X^2 0 2X^2 0 0 X^2 0 0 2X^2 X^2 0 0 0 X^2 2X^2 0 0 2X^2 2X^2 X^2 2X^2 X^2 0 X^2 X^2 0 2X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 2X^2 2X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 2X^2 X^2 0 0 X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 0 0 0 0 0 2X^2 0 2X^2 X^2 X^2 0 2X^2 2X^2 0 2X^2 X^2 2X^2 X^2 0 0 X^2 2X^2 0 2X^2 2X^2 0 2X^2 X^2 0 generates a code of length 61 over Z3[X]/(X^3) who´s minimum homogenous weight is 108. Homogenous weight enumerator: w(x)=1x^0+48x^108+48x^110+244x^111+312x^112+240x^113+1214x^114+1020x^115+600x^116+2430x^117+4038x^118+2316x^119+5060x^120+9534x^121+3546x^122+6588x^123+9720x^124+2700x^125+4016x^126+2712x^127+600x^128+1234x^129+360x^130+102x^131+146x^132+6x^133+48x^134+86x^135+6x^137+24x^138+16x^141+12x^144+8x^147+6x^150+4x^153+4x^159 The gray image is a linear code over GF(3) with n=549, k=10 and d=324. This code was found by Heurico 1.16 in 9.08 seconds.