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 X 1 1 X 1 1 1 1 1 1 1 1 X 1 X 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 X^2 2X^2 2X^2 X^2 0 X^2 X^2 2X^2 0 X^2 0 X^2 2X^2 2X^2 X^2 0 0 2X^2 0 X^2 2X^2 X^2 0 X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 X^2 X^2 0 X^2 0 0 2X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 2X^2 0 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 X^2 2X^2 0 X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 2X^2 0 0 X^2 0 2X^2 X^2 0 0 X^2 0 2X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 X^2 2X^2 2X^2 2X^2 X^2 0 0 0 X^2 X^2 2X^2 0 2X^2 X^2 X^2 X^2 0 X^2 2X^2 2X^2 2X^2 X^2 0 0 0 2X^2 X^2 0 0 0 X^2 2X^2 0 2X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 0 X^2 X^2 X^2 2X^2 X^2 X^2 2X^2 0 2X^2 X^2 X^2 2X^2 0 0 0 0 0 X^2 0 0 X^2 2X^2 0 2X^2 0 X^2 2X^2 0 X^2 2X^2 X^2 X^2 0 0 0 X^2 2X^2 X^2 0 X^2 2X^2 X^2 2X^2 0 2X^2 X^2 X^2 0 X^2 0 2X^2 0 2X^2 0 2X^2 X^2 2X^2 X^2 2X^2 0 0 X^2 X^2 X^2 0 2X^2 2X^2 X^2 X^2 X^2 X^2 X^2 2X^2 0 0 0 0 0 0 0 X^2 0 2X^2 2X^2 X^2 0 2X^2 X^2 0 2X^2 2X^2 0 X^2 2X^2 2X^2 0 2X^2 X^2 X^2 0 2X^2 0 X^2 2X^2 X^2 2X^2 0 2X^2 X^2 0 X^2 X^2 2X^2 0 X^2 X^2 2X^2 2X^2 2X^2 0 0 2X^2 0 2X^2 X^2 2X^2 0 2X^2 0 0 0 0 0 2X^2 0 2X^2 0 0 0 0 0 0 0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 2X^2 0 0 X^2 0 0 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 0 X^2 X^2 2X^2 0 0 2X^2 0 0 0 0 2X^2 X^2 2X^2 0 2X^2 X^2 X^2 0 2X^2 0 X^2 0 0 generates a code of length 62 over Z3[X]/(X^3) who�s minimum homogenous weight is 105. Homogenous weight enumerator: w(x)=1x^0+24x^105+128x^108+226x^111+226x^114+460x^117+732x^120+1834x^123+13122x^124+1520x^126+778x^129+154x^132+140x^135+114x^138+114x^141+40x^144+40x^147+24x^150+2x^153+2x^162+2x^171 The gray image is a linear code over GF(3) with n=558, k=9 and d=315. This code was found by Heurico 1.16 in 3.15 seconds.