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 1 0 1 2X 2X^2+X 1 1 1 1 1 1 1 0 1 1 1 0 X^2 1 1 1 1 1 1 2X 1 2X^2+X 1 2X 1 1 1 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 2X^2+1 1 2X^2+X+2 1 1 2X^2+2X+1 0 2X^2+X+2 2X 2X^2+X+2 X^2 2X+2 1 0 X^2+X+2 2X^2+2X+1 1 1 2X^2+2X+1 2X+2 0 2X^2+X 2X^2+1 X^2+2X+1 1 X^2+2X+1 1 X^2+2X+2 1 X^2+1 2X^2+X+2 2X X+1 X^2 2X^2+X 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 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 2X^2 X^2 2X^2 0 0 2X^2 X^2 X^2 0 0 X^2 0 2X^2 0 0 X^2 0 X^2 2X^2 0 X^2 0 2X^2 X^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 2X^2 X^2 2X^2 0 X^2 X^2 2X^2 2X^2 2X^2 0 0 X^2 2X^2 2X^2 0 0 0 X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 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 0 X^2 0 X^2 X^2 0 0 X^2 0 2X^2 X^2 2X^2 2X^2 0 0 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 0 2X^2 X^2 2X^2 0 2X^2 0 0 0 0 2X^2 X^2 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 2X^2 2X^2 0 0 0 X^2 0 2X^2 2X^2 X^2 0 0 0 X^2 0 2X^2 X^2 X^2 2X^2 2X^2 X^2 0 X^2 2X^2 0 2X^2 0 X^2 X^2 2X^2 0 2X^2 2X^2 2X^2 2X^2 generates a code of length 63 over Z3[X]/(X^3) who´s minimum homogenous weight is 114. Homogenous weight enumerator: w(x)=1x^0+114x^114+270x^115+36x^116+412x^117+1200x^118+630x^119+1178x^120+3450x^121+1980x^122+3080x^123+8154x^124+4500x^125+5378x^126+9894x^127+4230x^128+3828x^129+6078x^130+1746x^131+1024x^132+1296x^133+132x^135+246x^136+56x^138+30x^139+40x^141+32x^144+12x^147+8x^150+10x^153+2x^156+2x^162 The gray image is a linear code over GF(3) with n=567, k=10 and d=342. This code was found by Heurico 1.16 in 11.4 seconds.