The generator matrix 1 0 0 0 0 1 1 1 0 1 1 0 X 2X 1 1 1 1 1 X 1 1 2X 0 1 1 1 1 1 1 1 1 1 1 1 1 X 1 0 1 1 0 1 1 1 1 1 2X X 1 X 1 1 1 1 0 0 2X X 1 X 1 1 2X 1 1 1 1 0 1 0 0 0 0 0 0 X 2X X X 1 1 2 2 2X+2 2X+1 2X+2 1 2X+2 1 1 1 2 1 2 2X+1 2X+1 2X X+2 2 2X 2X 0 2X 1 2X+1 1 2 2X 1 X 2X X+1 2X 2 1 1 2X+2 1 X+2 X+1 2 X+2 1 1 1 2X 1 1 2 2 1 X+2 1 2X+2 0 0 0 1 0 0 0 1 2X+1 1 0 X+1 1 2 2X 2X+1 2X+2 2X 2 X+2 2X+1 X+1 X+1 1 2X+1 0 2X X+2 X+1 X 2X+2 X+2 X X+2 X X 2 X+2 1 X 2 2X+1 X+2 2X+1 2X+1 X X X+1 X+2 2X+1 2X+1 0 X 0 2X X+2 0 2X+1 2 1 X+1 X+1 X+1 2X+1 X+1 2X+1 X+2 2X X 0 0 0 1 0 1 1 2X+2 X+1 X X+2 X 2X+1 X+2 2X+1 0 2X+2 X+1 X+2 X+2 2X 2X+2 2X+2 2X+1 2X+1 0 X+2 2 2 2 X 1 X X+2 X+1 X+2 X+1 2X+1 2X+1 X+2 1 2 2X 2X 2X+1 0 X+2 0 X+2 2X+1 2X+2 2X X X+2 2X 2X+2 0 X 0 X 2X+1 2X 2X+2 0 2 1 2 2X 0 0 0 0 1 2 X 2X+2 X+1 1 1 2 2 2 2X+1 2 2 2X+1 2X+1 0 2X+2 2X 2X+2 2X+1 X X+1 2X X+2 X+2 X 0 2 2X+1 2X+1 2X X+1 0 2 2X+1 2X+2 1 X 2X+1 X+2 X+1 2X+1 X+2 X+1 2X+1 2 X+1 0 0 1 X+1 0 1 X+2 2X+2 X+1 2X X X+2 2X 2X+1 X 2X+2 2X 0 0 0 0 0 2X 0 2X X X X 2X 2X 2X X 2X 2X X X 0 2X X X 0 2X 2X 2X 0 X X X 0 0 2X X 2X 2X X 2X X 2X X 2X X X 0 X 2X X X 2X X 2X 2X 2X 2X X 0 0 0 2X X 2X 0 0 0 0 0 generates a code of length 68 over Z3[X]/(X^2) who´s minimum homogenous weight is 117. Homogenous weight enumerator: w(x)=1x^0+140x^117+156x^118+462x^119+1020x^120+1020x^121+1296x^122+2642x^123+2310x^124+2760x^125+4492x^126+3810x^127+4500x^128+7326x^129+5904x^130+6618x^131+9952x^132+8094x^133+8112x^134+11596x^135+8790x^136+9486x^137+11804x^138+8718x^139+8016x^140+10520x^141+6720x^142+6246x^143+7328x^144+4362x^145+3306x^146+3574x^147+1824x^148+1290x^149+1278x^150+642x^151+324x^152+384x^153+108x^154+66x^155+84x^156+30x^157+6x^158+10x^159+8x^162+4x^165+6x^168+2x^174 The gray image is a linear code over GF(3) with n=204, k=11 and d=117. This code was found by Heurico 1.16 in 533 seconds.