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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 X 1 X 1 1 1 2X^2 1 X 1 1 0 1 1 1 1 X 1 X 0 X 0 0 2X 2X^2+X X 2X^2+2X 2X X^2 2X^2 2X^2+X 2X^2+X 2X^2+2X 2X 2X^2 X^2+X 2X^2+2X X 2X^2+X X 2X X^2 X^2+2X 0 2X^2+2X 2X^2+X X^2 X X X^2+X X X^2 2X^2+X 2X^2+X X^2 2X^2 X 2X^2+X X^2+2X X^2+2X X^2+2X X^2+2X X^2+2X 0 2X^2 2X^2 2X^2+2X X^2+2X 2X 2X^2 2X 0 2X^2 0 0 X^2+2X 2X^2+2X X^2+2X 2X^2 2X^2+2X X^2 X^2+X 0 X^2 2X^2+2X X^2 2X^2+X 2X^2+X X^2+X X^2+2X X^2 X^2+X 2X^2+2X 2X^2+2X X 0 2X 2X 2X^2+X X^2+2X 2X^2+2X 0 X 2X^2+2X 2X X X^2+X X 2X 2X^2+X 2X 2X^2+2X X^2+X 0 2X^2+X 0 0 X 2X X^2 2X^2+2X X 2X^2+X X^2+2X 2X^2+2X 0 2X^2+2X X^2 2X X^2 X X X^2+X 2X 0 X^2+X 2X 2X^2+2X X^2+X X^2+X 2X^2 0 0 2X^2+2X X 2X^2+X X^2 X^2 X^2+2X 2X 2X^2+X 2X^2+2X X^2+X 2X^2 2X^2+X 2X^2 2X X^2 X^2+X 0 2X X^2+X 2X^2+2X X^2 2X 0 X X^2+X 2X X^2 X^2 X X^2+2X 2X^2 2X^2+2X X^2+X X 0 X 2X X^2+2X X X^2+X X^2+2X X^2+X X 2X X^2+2X X^2 X^2+X X X 2X^2+2X 0 X^2+2X 2X^2+2X 2X^2+2X 2X^2+X X 2X^2+X 2X^2 X^2+2X X 2X^2+2X 0 2X^2 X^2+2X 2X^2 0 X^2+2X 2X 0 0 0 X^2 0 0 0 0 0 0 2X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 0 2X^2 0 X^2 X^2 0 0 X^2 2X^2 2X^2 2X^2 0 0 X^2 2X^2 0 0 X^2 X^2 0 X^2 2X^2 X^2 0 2X^2 2X^2 0 X^2 X^2 X^2 0 X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 0 X^2 0 2X^2 X^2 0 X^2 0 X^2 2X^2 0 0 2X^2 X^2 X^2 X^2 2X^2 0 0 0 0 0 X^2 2X^2 0 0 2X^2 generates a code of length 96 over Z3[X]/(X^3) who´s minimum homogenous weight is 184. Homogenous weight enumerator: w(x)=1x^0+138x^184+156x^185+138x^186+360x^187+378x^188+504x^189+474x^190+618x^191+1366x^192+498x^193+582x^194+608x^195+258x^196+84x^197+18x^198+96x^199+36x^200+12x^201+24x^202+18x^203+10x^204+48x^205+24x^206+8x^207+42x^208+48x^209+6x^210+6x^211+2x^264 The gray image is a linear code over GF(3) with n=864, k=8 and d=552. This code was found by Heurico 1.16 in 0.873 seconds.