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 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 X 1 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 2X^2 2X^2 X^2 2X^2 X^2 2X^2 0 X^2 0 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 0 2X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 2X^2 0 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 0 X^2 0 2X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 2X^2 0 2X^2 0 0 X^2 0 0 0 0 0 0 0 0 X^2 2X^2 2X^2 2X^2 2X^2 0 X^2 X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 0 0 X^2 0 2X^2 X^2 X^2 X^2 0 0 0 2X^2 2X^2 2X^2 0 2X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2 0 0 0 2X^2 X^2 0 0 X^2 0 2X^2 2X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 X^2 2X^2 2X^2 2X^2 0 0 X^2 0 X^2 2X^2 2X^2 0 2X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 X^2 0 X^2 X^2 0 2X^2 X^2 X^2 2X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 2X^2 2X^2 2X^2 X^2 0 X^2 2X^2 X^2 X^2 0 X^2 X^2 2X^2 2X^2 0 0 2X^2 2X^2 X^2 2X^2 0 0 0 0 X^2 0 0 X^2 2X^2 0 2X^2 0 0 2X^2 2X^2 X^2 X^2 X^2 0 X^2 X^2 2X^2 X^2 2X^2 2X^2 0 X^2 X^2 X^2 2X^2 2X^2 2X^2 0 0 0 2X^2 2X^2 X^2 2X^2 2X^2 0 0 0 2X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 0 X^2 0 X^2 0 0 0 0 2X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 2X^2 2X^2 X^2 0 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 0 0 X^2 0 2X^2 2X^2 2X^2 X^2 2X^2 0 2X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 2X^2 X^2 2X^2 0 0 0 X^2 0 X^2 2X^2 X^2 0 2X^2 X^2 2X^2 2X^2 0 X^2 2X^2 0 2X^2 X^2 2X^2 X^2 2X^2 0 0 0 0 0 0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2 0 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 X^2 2X^2 X^2 X^2 X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 X^2 2X^2 X^2 X^2 2X^2 2X^2 2X^2 0 0 X^2 2X^2 X^2 0 0 X^2 2X^2 2X^2 X^2 2X^2 0 2X^2 2X^2 X^2 X^2 0 0 2X^2 0 2X^2 generates a code of length 64 over Z3[X]/(X^3) who´s minimum homogenous weight is 111. Homogenous weight enumerator: w(x)=1x^0+96x^111+192x^114+230x^117+208x^120+162x^122+220x^123+972x^125+188x^126+15066x^128+180x^129+1296x^131+174x^132+180x^135+140x^138+132x^141+104x^144+64x^147+32x^150+26x^153+12x^156+6x^159+2x^183 The gray image is a linear code over GF(3) with n=576, k=9 and d=333. This code was found by Heurico 1.16 in 3.34 seconds.