The generator matrix 1 0 1 1 1 X^2 1 1 0 0 1 1 1 0 1 X^2 1 1 1 1 0 1 0 1 1 X 1 X 1 X 1 X 1 1 0 1 1 1 1 1 X^2+X X 1 X^2+X 1 X^2+X X 1 1 1 1 0 X^2 1 X 1 0 1 X^2 1 X 1 1 X^2+X 1 1 X X^2 1 0 1 1 1 1 1 1 X^2 0 X^2+X X 1 X^2 1 0 1 X X 1 X^2 1 0 1 1 0 1 1 X^2 X+1 1 1 0 X^2+X+1 X^2+1 1 0 1 X^2 1 1 0 1 X^2+1 1 X X+1 1 X 1 X^2+X+1 1 X 1 X+1 0 1 X+1 X^2+X X+1 X+1 X^2+X 1 1 X+1 1 1 1 1 X^2+X 1 X+1 0 1 1 X^2+X 1 X^2 1 0 1 X 1 X^2 X^2+X 1 X 0 1 1 X+1 1 X^2+1 0 X X X^2+X+1 X 1 1 1 1 1 1 X X X^2+X+1 1 1 X 0 0 0 0 X 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X X^2+X X^2+X X X X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X^2 0 X^2+X X^2+X 0 X^2 0 0 X^2+X X^2 0 X^2+X X^2+X X^2 X^2 X X^2+X X^2+X 0 0 X^2 0 0 X^2 X^2 X X^2+X X 0 X X^2 X^2+X X 0 X^2+X X^2 X X X X^2 X^2 0 X X^2 X^2+X 0 X X^2+X X^2 X X^2 X^2+X 0 X^2 X^2+X 0 X^2 X^2+X 0 X X^2+X X X X 0 0 0 0 X 0 0 X^2 X^2 X X X^2+X X^2+X X^2+X X^2+X X^2 X^2+X X^2+X X 0 X X^2 X^2+X 0 0 X^2+X 0 0 X^2 X X^2 0 X^2+X X^2 X^2+X X 0 X^2 X X 0 X^2 X^2+X 0 X X^2 X^2+X 0 X X X^2 X^2+X X^2 0 X X^2+X 0 X X^2+X X X^2+X X^2+X 0 X^2+X X X^2+X 0 X X^2 X X^2+X X^2+X X^2 0 X^2 X^2 X 0 0 X^2 X 0 X^2+X X X X X^2+X X^2+X X^2 X^2+X 0 0 0 0 0 X X^2+X X^2+X X^2 X^2+X 0 X^2+X 0 X X^2 X^2+X X^2+X X X^2+X X X^2 X 0 X^2 X^2 X^2 X^2+X X^2+X X^2+X X X^2 X^2 0 X X X X^2 X 0 X X X^2 0 0 X 0 0 X^2+X X^2+X 0 X^2+X X^2 0 X X X X 0 X^2+X 0 X^2+X X^2 X^2 X^2+X X 0 X^2 X^2+X 0 0 0 X X^2 X^2+X X^2 X^2 0 X^2+X X^2 X X^2 0 X^2 X^2+X X^2 X X X^2 0 0 0 generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 82. Homogenous weight enumerator: w(x)=1x^0+100x^82+108x^83+257x^84+240x^85+397x^86+232x^87+370x^88+244x^89+413x^90+206x^91+332x^92+206x^93+335x^94+174x^95+207x^96+58x^97+82x^98+28x^99+28x^100+12x^101+10x^102+14x^103+18x^104+6x^105+4x^106+6x^107+2x^108+2x^109+2x^110+1x^116+1x^130 The gray image is a linear code over GF(2) with n=360, k=12 and d=164. This code was found by Heurico 1.16 in 1.59 seconds.