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 X 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X X 2X 2X 2X X 2X 2X X X X 0 X X X 2X 0 0 2X X X 2X 0 2X 0 X X X 2X 0 0 X X 2X 0 X 0 0 0 2X 2X 2X X X X 0 0 2X X 0 2X X X 0 0 0 X 0 X X 0 X 2X 0 2X X X 0 X 0 2X 2X 2X X 0 0 X 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X 0 X 0 X X 2X 2X 0 X X 2X 2X 2X 2X 2X 2X X 2X 0 X 2X 0 2X 0 X X 0 2X 0 X X X X 0 2X 0 0 X X X 2X 2X X X X 2X X 2X 2X 0 0 2X 0 X X 2X X 0 2X 0 0 2X 0 2X 2X 0 0 0 2X 2X 2X 2X 2X X 0 0 0 X 0 0 0 0 X 2X 2X 2X 0 0 X 0 X 2X X 2X 2X 2X 0 X X 0 2X X 0 0 0 X X X 2X 2X 2X 0 X 0 0 2X 2X 0 2X X X 0 X 0 X 2X 0 0 X X 0 2X X 0 X 2X 2X 0 2X 2X 0 X X 0 X X X 0 2X X X 0 0 2X X X 0 0 0 0 2X X 0 X 0 0 0 0 X 0 0 X 2X 0 2X 0 0 2X 2X X X X 2X X 0 2X 2X X 0 0 0 X 0 0 2X X X X 0 0 2X 0 2X 2X 2X 0 2X X X 2X 0 X 2X X X 2X 2X X X 0 0 0 2X 0 2X X 2X X 0 X 0 2X 0 2X X X 0 0 X 0 X X X X 0 X 0 2X 0 X X 2X X X 0 0 0 0 0 X 0 2X 2X X 0 2X 2X 2X 2X 2X 2X 0 X 0 0 2X 0 2X X X 2X 2X X 0 0 2X 2X 2X 2X 0 0 2X X 0 2X 0 2X X 2X 0 X X X 2X X 2X 2X 0 0 2X 0 0 2X X 0 2X 0 X 0 0 X 2X X 0 0 X 0 X 0 0 X 0 X 2X X 2X 0 2X 2X 0 X X 2X X 0 0 0 0 0 0 X 2X 2X 2X 2X 2X 2X X X X 0 2X 0 0 X 0 2X X X X X 2X 0 0 X 2X 0 X 2X 2X X X 2X 2X 0 X 2X X 0 X 0 X 2X X X X X 0 X 2X 0 X 2X 0 X X 0 X 2X 0 X 2X 2X X 0 2X 0 2X X 2X 0 0 0 2X 2X X X 2X X 0 0 0 0 X generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 162. Homogenous weight enumerator: w(x)=1x^0+112x^162+212x^165+198x^168+230x^171+380x^174+1150x^177+2100x^180+1456x^183+104x^186+122x^189+114x^192+100x^195+74x^198+80x^201+54x^204+32x^207+24x^210+14x^213+2x^219+2x^261 The gray image is a linear code over GF(3) with n=270, k=8 and d=162. This code was found by Heurico 1.16 in 2.39 seconds.