The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 X^2+X 1 1 1 0 1 X^2+X 1 1 1 0 1 1 X^2+X 1 1 0 1 1 X^2+X 1 1 1 1 X^2 1 1 X^2+X 1 1 1 X 1 0 1 1 1 1 X^2 1 1 X 1 0 1 1 1 1 1 X^2+X X 1 1 X 1 1 1 1 1 1 1 1 X 1 1 1 0 1 1 X^2 X^2+X 1 1 1 1 X 0 1 X 1 1 X 1 1 0 1 X^2 X^2+X 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X 1 X^2+1 0 X+1 1 X^2+X 1 X^2+1 X^2+X+1 0 1 X^2+1 X^2+X 1 X^2+1 0 1 X+1 X^2+X 1 1 X+1 X+1 X 1 X^2+1 0 1 X^2+1 X+1 X^2 1 X^2+X 1 X^2+1 X+1 X^2+X+1 X^2+X 1 X+1 0 1 X^2+1 1 X^2 1 X+1 1 X^2+X+1 1 1 X^2 X^2 1 1 X^2+X+1 X+1 X^2+1 X^2+1 X+1 X X^2+X+1 0 X^2+1 X^2 0 1 X X 1 1 X^2+X+1 0 X X^2+1 0 X 0 1 X^2+1 1 1 X^2+X X X^2 X^2+1 X^2 1 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 generates a code of length 98 over Z2[X]/(X^3) who´s minimum homogenous weight is 89. Homogenous weight enumerator: w(x)=1x^0+56x^89+169x^90+98x^91+308x^92+114x^93+432x^94+120x^95+452x^96+138x^97+409x^98+126x^99+506x^100+106x^101+355x^102+122x^103+211x^104+82x^105+154x^106+40x^107+45x^108+12x^109+8x^110+6x^111+6x^112+4x^113+3x^114+3x^116+2x^118+1x^120+1x^122+1x^124+2x^126+1x^128+1x^132+1x^134 The gray image is a linear code over GF(2) with n=392, k=12 and d=178. This code was found by Heurico 1.16 in 72.9 seconds.