The generator matrix 1 0 0 0 0 1 1 1 0 1 X^2 1 X^2 1 X^2+X 1 0 1 1 X 1 X^2+X X 1 0 X X 1 1 1 1 1 0 X^2 1 1 1 0 0 0 1 X^2+X 1 1 1 1 1 X^2+X X^2+X 1 X^2+X X 1 X^2 X X^2 1 X^2 X^2 X^2+X X 0 0 1 1 1 1 1 X^2+X X 1 1 1 0 X^2 X X^2 1 X^2 X^2 X 1 0 1 0 0 0 0 0 X^2 X^2 1 1 1 1 1 1 X+1 X^2+X X^2+X+1 X^2+X X X+1 1 1 X^2 1 0 1 X+1 X^2+X X^2 X^2+1 X^2+1 X^2 X X^2+X X^2+X X^2 1 1 0 1 0 X+1 X^2+X X X+1 X^2+1 1 1 X^2+X X^2+X 0 X 1 1 0 X+1 1 1 X X^2+X 1 1 X X^2+X+1 X^2+X X^2+X X X^2+X 1 X^2+1 0 X+1 0 X 1 1 X^2+X+1 1 X X 0 0 0 1 0 0 X^2 1 X^2+1 1 0 1 X+1 X^2+X+1 X^2+1 0 X 1 X X^2+X+1 1 X+1 0 X X X^2+X+1 X^2+X X+1 X^2+X X+1 X^2 1 X^2+1 1 1 X^2+X X X^2+X+1 X^2 X^2+X+1 1 X^2+X 0 0 X^2+1 X^2 X^2+X X^2+X+1 X 0 1 X 1 X^2 X^2+X+1 0 X^2+X X^2+X+1 X^2 X+1 1 1 0 1 X+1 X 1 X^2+X 1 X^2 X+1 X^2 X^2+1 X^2 X^2 X^2+X X^2+X X^2+1 X^2 X^2+X+1 1 1 0 0 0 0 1 0 X^2+1 1 0 1 X^2 X^2+1 X+1 X^2 X^2+X X^2+1 X^2+X+1 X^2+X 1 0 X^2+X+1 X^2+1 X^2+X X+1 0 0 1 X+1 X X^2+1 X^2+1 1 X X+1 X+1 X^2+X X^2+X+1 X^2+X X^2 X^2+X X X 0 X+1 X+1 X^2+X+1 1 X^2+X X^2 X+1 X+1 1 X^2 0 0 X X^2 X+1 X^2+X+1 1 1 X X^2 1 1 X^2+1 X^2+X X^2 X^2 1 0 X 1 0 1 1 X^2+X+1 1 X+1 0 X^2+1 X^2+X 0 0 0 0 0 1 1 X^2 1 1 X^2+1 X^2 1 X+1 0 1 0 X^2+1 X+1 X^2+X X^2+X X^2+X X^2+X+1 0 X^2+X+1 X X+1 X+1 X X+1 X^2+X+1 X X^2+X+1 X^2+X+1 0 X^2+1 X^2 X^2+1 X X^2+X X^2+1 X 1 X+1 1 X^2+X+1 X^2+1 X^2+X X^2+X+1 X^2+X X X^2+X X^2 X^2 X^2 X^2 1 X 1 X^2 X+1 X^2 X^2+X+1 X^2+1 X^2+1 0 X^2+X+1 X+1 X 0 X^2+X+1 X^2+1 X^2+X X+1 X^2+X+1 X^2+1 X^2+1 X+1 X^2+X X^2+1 X^2+X X 0 generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+138x^72+456x^73+830x^74+1204x^75+1565x^76+1778x^77+2041x^78+2190x^79+2379x^80+2682x^81+2677x^82+2478x^83+2360x^84+2290x^85+1947x^86+1782x^87+1368x^88+934x^89+679x^90+382x^91+295x^92+166x^93+76x^94+22x^95+22x^96+12x^97+6x^98+4x^99+2x^101+2x^103 The gray image is a linear code over GF(2) with n=328, k=15 and d=144. This code was found by Heurico 1.13 in 17.7 seconds.