The generator matrix 1 0 0 1 1 1 1 X 1 1 2X 1 1 1 0 1 1 1 1 1 1 2X X 1 0 1 1 2X 1 1 1 0 X 1 1 1 2X 1 1 1 1 1 1 2X 1 1 X 0 2X 1 2X 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 X 1 1 1 1 0 1 1 1 1 X 0 1 1 1 2X 2X 1 1 1 1 1 2X 1 1 1 1 1 0 1 0 0 0 2X+1 1 1 2X+2 2X+1 1 2 2 X 2X 2X X 2X+2 X+1 1 1 1 1 2X+2 1 2 1 1 X 0 2X+1 1 1 X+1 X 1 X 2X+1 X+2 0 2X+2 X X 1 X 0 1 1 1 X+1 1 X X+1 0 X+1 1 0 1 X 2X 1 2X 2X+2 2X+1 2 2X+1 2X 0 X 2X+2 X 2 2 1 X+2 2X+2 X+1 X+2 1 1 X 2X 0 1 1 2 2X 2 X+1 0 0 X+1 X+2 X+2 2X+1 0 0 0 1 1 2 2X+2 1 X+2 2X+1 2X 1 X X+2 X+2 1 0 X+1 X+1 X X+2 1 2 X+1 X X X+2 0 2X 2X 1 X+1 X+2 1 X+1 2X+1 2X+2 1 0 0 0 X+2 1 2 X 2 2X X+2 1 2X+1 2 0 X 1 X+2 2 2X+1 2X+2 2 2X 1 0 1 X+1 X+2 0 2 X+1 1 1 2X 2 2X+2 X+2 1 2X+2 2X+1 X 2X+1 0 2X+2 X+1 X X 2X 2X 1 0 2X+1 2X+2 2X 1 2X+2 2X 2X 1 0 0 0 0 2X 0 0 0 0 0 2X X 0 0 0 X 2X X 2X X X 0 0 0 0 X 2X X 2X 0 2X 2X 2X X 2X X X X 0 2X X 2X 0 X 2X X X X 0 2X X 0 2X X X 2X 0 2X 2X 2X 2X 2X 0 X 0 X 2X X 0 2X X 2X 0 X 2X 0 0 2X X 2X 0 0 X X 2X 0 2X 2X X 2X 0 2X 0 X 0 X 2X 0 0 0 0 X X X 0 X 0 X 0 2X 0 X 0 X 0 0 0 2X 2X 2X 2X X 2X X 2X 2X 2X X 0 2X 2X 0 2X 2X 0 0 2X X 0 2X X 0 X 2X X 2X X X 2X 0 X 0 0 0 X X 2X X 2X 0 0 0 2X 2X 2X X 2X X 0 0 X X 0 0 X 2X 2X X X 2X 0 X 0 X 2X 2X X X 0 X 0 2X 0 generates a code of length 96 over Z3[X]/(X^2) who´s minimum homogenous weight is 180. Homogenous weight enumerator: w(x)=1x^0+122x^180+114x^181+132x^182+490x^183+264x^184+258x^185+630x^186+204x^187+228x^188+536x^189+222x^190+216x^191+504x^192+180x^193+216x^194+344x^195+132x^196+132x^197+342x^198+72x^199+102x^200+302x^201+108x^202+90x^203+140x^204+66x^205+48x^206+140x^207+60x^208+18x^209+64x^210+24x^211+12x^212+18x^213+12x^214+6x^215+2x^216+6x^219+2x^222+2x^228 The gray image is a linear code over GF(3) with n=288, k=8 and d=180. This code was found by Heurico 1.16 in 1.02 seconds.