The generator matrix 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 1 1 0 1 1 1 0 0 1 1 2X 1 1 1 1 1 2X 1 1 X X 1 1 1 0 2X 1 2X 2X 0 0 1 1 2X 1 1 0 X 1 1 1 1 0 1 1 0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 1 X+2 0 2X+1 0 2X+1 2 1 0 2 2X+1 1 1 X X 1 2 2X+1 X+1 2X+2 2X 1 0 X+1 1 1 2 X+1 2X+1 1 1 2X 1 1 1 1 2X+2 2X 1 2X 2X+1 X 1 1 1 1 2 1 0 0 0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 2X 0 2X 2X 0 2X 2X 0 2X 0 X 0 2X 0 0 X 2X 2X X 0 X 2X 2X 0 X 2X X 0 2X 0 2X 2X 2X X X 2X 0 X X 0 2X 0 X 2X X X 0 2X X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X 2X X 0 X X 2X 2X X 0 X X 0 X 0 X 0 2X X X X 0 2X X X 2X X X 0 X 0 X 0 X 2X X 2X 0 2X 0 X 2X X 0 0 2X 0 2X 2X 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 2X 2X X 0 2X X 2X 0 2X X 2X 0 2X 2X 0 2X 2X X 2X 2X X 0 2X 0 2X 2X 0 X 0 X 2X 2X 0 X 2X X 0 X 2X 2X 2X X X 0 X 0 0 2X 0 2X X 0 0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X 2X X 0 0 0 X X X 0 0 0 X 2X X 2X 2X 0 0 2X X 0 X X X X X 0 2X X 0 2X X X 2X 0 X 0 0 2X 2X 2X 2X X 0 0 0 2X 0 2X 0 0 0 0 0 0 0 X 0 X 0 X X X 2X 2X 0 X 2X 2X 0 2X X 2X 0 0 2X X 2X 0 2X X 0 2X X 2X X 2X 0 0 0 X 2X 2X 0 2X 0 X X 2X 0 2X X 2X X 2X 2X 2X X 0 0 2X X 2X 0 X 0 0 0 0 0 0 0 0 X X X X 0 2X X 2X X X X X 2X 2X 2X X 0 X X 2X X X 0 0 X 0 0 X 0 X 0 0 2X 0 2X X X X 2X X X 2X X 0 0 0 2X 2X 0 0 X X 2X 0 0 2X X 2X 0 generates a code of length 66 over Z3[X]/(X^2) who´s minimum homogenous weight is 108. Homogenous weight enumerator: w(x)=1x^0+48x^108+188x^111+42x^112+30x^113+350x^114+114x^115+222x^116+342x^117+444x^118+606x^119+434x^120+984x^121+1410x^122+476x^123+1806x^124+2448x^125+576x^126+3522x^127+3858x^128+562x^129+5142x^130+4998x^131+594x^132+5280x^133+5040x^134+578x^135+4194x^136+4092x^137+622x^138+2994x^139+2304x^140+490x^141+1206x^142+876x^143+426x^144+420x^145+354x^146+324x^147+72x^148+6x^149+264x^150+18x^151+152x^153+6x^154+76x^156+38x^159+8x^162+8x^165+2x^168+2x^171 The gray image is a linear code over GF(3) with n=198, k=10 and d=108. This code was found by Heurico 1.16 in 56.5 seconds.