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 1 1 X^2 1 X^2+X 1 0 0 1 1 X X X 1 X 1 X^2 1 1 1 X^2+X 0 0 X^2+X 1 1 1 0 1 0 1 X^2 0 X^2+X X^2 X^2 1 X^2 1 1 0 1 1 1 X^2+X X X 1 1 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 1 X^2+X X 1 1 1 X^2+1 1 0 X 0 X^2 0 X^2+X X+1 0 X^2+X 1 X^2 X^2+1 X^2+1 X^2 X 1 X X^2+X+1 0 X 0 X^2+1 1 X^2+1 1 1 1 X X X+1 X^2+X 0 0 1 X+1 1 1 X^2+X 1 1 X X^2+1 1 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 X^2+1 X X^2 X X+1 1 X+1 X X X X^2+X+1 0 X 1 X X 1 X^2+1 0 X^2+1 X^2+X X^2+X+1 0 X^2 X^2 X^2 X^2+X+1 0 X^2+1 1 1 X^2+X+1 1 X^2+X+1 1 X^2 1 1 X^2+X+1 1 X^2+1 1 X^2+X+1 0 0 X^2 1 X X^2 X^2+X X^2+1 0 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 X X^2+X X+1 X X^2+1 X X^2+1 X+1 X^2+X+1 1 X^2 X^2 1 0 X X+1 X^2+X X^2+X+1 X^2+X X^2+X X+1 X^2+X 1 X^2+X X^2+1 1 X^2 X^2+X+1 X^2+X X^2+X X^2+X+1 X+1 0 X^2 1 0 X^2+1 1 X^2+X+1 X^2+X+1 X^2+X X^2+X+1 X^2+X 0 X^2 X X^2+1 0 0 0 X^2 X^2 X^2 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^2+1 X+1 X 1 X^2+X X X^2+X+1 0 X 1 X^2 X X X^2+X+1 1 X^2+1 X X X^2+1 X^2+1 1 X+1 X+1 1 X^2 X^2+1 X^2+1 X^2+X+1 1 X^2+X X+1 X^2+1 X^2+X+1 X^2+1 X^2+X+1 X^2+X 1 X^2 X X^2+X X^2+X+1 1 X^2+X X X+1 X^2+X+1 X+1 X X+1 X 0 X^2+1 0 generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 73. Homogenous weight enumerator: w(x)=1x^0+80x^73+523x^74+748x^75+1278x^76+1478x^77+1865x^78+1972x^79+2360x^80+2320x^81+2619x^82+2424x^83+2787x^84+2230x^85+2477x^86+1898x^87+1861x^88+1238x^89+1032x^90+614x^91+413x^92+286x^93+136x^94+52x^95+32x^96+14x^97+18x^98+2x^99+2x^100+2x^101+2x^102+2x^103+2x^104 The gray image is a linear code over GF(2) with n=332, k=15 and d=146. This code was found by Heurico 1.13 in 18 seconds.