The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 X 1 0 1 X 1 1 1 X 1 1 1 X 1 1 1 1 1 1 1 1 X X 1 1 0 X 2X 0 2X^2+X 2X 0 2X^2+X 2X X^2 2X^2+X 2X X^2+2X 0 2X^2+X X^2+X X^2+2X X^2 2X 0 2X^2+X X^2+X 0 2X X^2 X X^2+2X 2X^2+2X X^2 2X 0 2X^2+X 2X^2 X^2+X X^2 X^2+2X 2X 2X^2+X X X 0 X^2+2X 2X^2+2X 2X X^2 X 2X^2 2X^2+X X^2+2X 2X^2+2X 2X^2+X 2X X^2+2X 2X^2+2X 0 2X^2+X 2X^2+2X X^2+2X X^2 2X^2+X X 2X^2 2X 2X^2+X 2X 2X^2+X 2X^2+2X 2X^2+X 0 0 X^2 0 0 0 0 2X^2 X^2 0 X^2 2X^2 2X^2 0 0 X^2 0 0 X^2 2X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2 0 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 2X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 2X^2 0 0 2X^2 0 2X^2 2X^2 0 2X^2 X^2 0 0 X^2 2X^2 X^2 X^2 X^2 X^2 2X^2 0 0 0 0 0 X^2 0 0 0 0 0 2X^2 0 X^2 2X^2 X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 0 2X^2 X^2 0 X^2 X^2 2X^2 2X^2 X^2 2X^2 0 2X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 2X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 0 0 0 0 2X^2 0 X^2 2X^2 X^2 X^2 0 X^2 2X^2 0 2X^2 0 2X^2 0 2X^2 2X^2 0 0 2X^2 X^2 X^2 0 0 2X^2 2X^2 2X^2 0 2X^2 2X^2 X^2 2X^2 X^2 0 0 0 X^2 2X^2 X^2 2X^2 2X^2 0 X^2 X^2 0 2X^2 2X^2 X^2 0 2X^2 0 2X^2 X^2 0 0 X^2 X^2 2X^2 2X^2 0 X^2 2X^2 0 0 X^2 0 0 0 0 0 X^2 X^2 0 2X^2 X^2 0 0 X^2 X^2 2X^2 2X^2 X^2 X^2 0 2X^2 0 0 2X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 2X^2 0 X^2 0 X^2 X^2 2X^2 X^2 0 2X^2 2X^2 X^2 2X^2 X^2 0 2X^2 X^2 2X^2 0 X^2 2X^2 2X^2 X^2 0 2X^2 X^2 0 0 0 2X^2 X^2 0 0 0 0 2X^2 X^2 generates a code of length 68 over Z3[X]/(X^3) who´s minimum homogenous weight is 123. Homogenous weight enumerator: w(x)=1x^0+88x^123+48x^124+96x^125+240x^126+144x^127+222x^128+434x^129+312x^130+642x^131+584x^132+1212x^133+2946x^134+666x^135+2226x^136+4890x^137+688x^138+1566x^139+1080x^140+414x^141+144x^142+198x^143+198x^144+114x^145+126x^146+188x^147+66x^148+6x^149+68x^150+24x^153+18x^156+16x^159+10x^162+4x^165+2x^171+2x^180 The gray image is a linear code over GF(3) with n=612, k=9 and d=369. This code was found by Heurico 1.16 in 2.49 seconds.