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 1 1 0 1 1 1 2X 1 1 1 1 2X^2+X 1 2X 1 1 1 2X 1 0 1 1 0 1 1 2X^2+X 1 X^2 1 2X^2+X 1 X^2+X 1 1 1 1 X^2+X 1 1 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 X+1 2 2X^2+X 2X+2 1 2X^2+1 2X^2+X+2 0 1 2X^2+2X+1 2X X^2+2 2X^2+1 1 2X^2+X 1 2X^2+2X+1 2 2X^2+X+2 1 2X 1 X^2+X+2 X+1 1 X+1 2X^2+X+2 1 2 1 X^2+2 1 0 1 X^2+X+1 2X 2X^2+2X+1 X^2+2X+1 1 X^2+X+2 2X^2+X X^2+X+2 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 0 0 X^2 2X^2 0 X^2 X^2 2X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 2X^2 0 X^2 X^2 X^2 0 2X^2 0 0 0 X^2 X^2 X^2 2X^2 2X^2 0 X^2 X^2 2X^2 0 X^2 0 0 X^2 2X^2 X^2 2X^2 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 2X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 X^2 X^2 0 2X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 2X^2 0 2X^2 X^2 2X^2 0 2X^2 0 2X^2 0 2X^2 2X^2 0 X^2 X^2 2X^2 0 0 X^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 0 X^2 2X^2 2X^2 0 2X^2 2X^2 0 2X^2 2X^2 X^2 0 X^2 X^2 0 2X^2 2X^2 X^2 X^2 X^2 X^2 X^2 2X^2 X^2 0 0 0 X^2 X^2 2X^2 0 X^2 0 X^2 0 0 0 2X^2 X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 2X^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 X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 0 0 X^2 0 0 2X^2 0 X^2 0 2X^2 2X^2 2X^2 X^2 0 2X^2 0 X^2 0 2X^2 2X^2 0 0 X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 0 2X^2 X^2 X^2 X^2 2X^2 generates a code of length 66 over Z3[X]/(X^3) who´s minimum homogenous weight is 120. Homogenous weight enumerator: w(x)=1x^0+166x^120+90x^121+198x^122+666x^123+696x^124+1086x^125+1670x^126+2124x^127+3144x^128+4456x^129+5130x^130+5658x^131+6712x^132+6204x^133+5844x^134+5402x^135+4014x^136+2736x^137+1616x^138+612x^139+246x^140+240x^141+66x^142+36x^143+100x^144+18x^145+6x^146+44x^147+24x^150+14x^153+8x^156+8x^159+4x^162+10x^165 The gray image is a linear code over GF(3) with n=594, k=10 and d=360. This code was found by Heurico 1.16 in 27 seconds.