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 X 1 X X X^2 X 1 0 1 X^2 X^2 0 0 1 1 1 X 1 X^2 1 0 X X 1 1 1 X^2 X 0 1 1 X 1 X 1 X 1 1 1 0 X^2 X^2 X 1 1 0 1 1 1 X 1 1 1 1 1 1 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X 0 X^2+X X X^2 X^2+X X^2+X 0 0 X X^2+X X^2 X^2 0 0 X^2+X X X^2+X 0 0 X^2 X X^2+X 0 0 X X^2+X X 0 X^2 X^2+X X^2 X X X X^2 X^2 X X X X X^2 0 0 0 X X^2 X 0 X 0 0 X^2+X X^2 0 0 X^2 X X X^2 X^2 X X^2 X^2 X X^2+X X 0 X^2+X X X^2 X X 0 X X 0 X X^2+X X^2 X^2 0 X^2 X^2+X X^2+X 0 0 0 X 0 X X X^2+X 0 0 0 X X^2 X X^2+X X^2 X^2+X X^2 X^2 X^2 0 X X X^2+X X X X X^2+X X^2 X^2 X X^2 X^2+X 0 X X^2+X 0 X X^2 X^2+X 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^2 0 X^2+X X^2+X X^2 0 X 0 X X X X^2 0 X^2 0 0 X^2 X^2+X 0 0 X^2 X^2+X X^2+X 0 X 0 X 0 X X^2+X 0 X X X X^2 X^2 0 X^2 X X^2+X X 0 X 0 0 0 0 X X 0 X^2+X X 0 X 0 X X^2+X X^2+X X^2 X^2 0 X^2 X X^2+X 0 0 X^2+X X 0 0 X X^2+X 0 X X X 0 0 X^2 0 X^2+X X^2+X X^2 X^2 X^2 X^2 X^2+X X^2+X X^2 0 0 X^2+X X^2 0 0 X X^2 X X X X X^2+X X^2+X X^2 X^2 X X^2+X X X^2+X 0 X^2+X X X X^2+X X^2+X X^2 X^2 X^2+X X X X 0 X^2+X 0 X X^2+X X^2 X^2 X 0 X^2 X^2 X^2 X 0 X^2+X X^2+X 0 0 X^2 X 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 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 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 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 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 generates a code of length 98 over Z2[X]/(X^3) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+56x^84+54x^85+151x^86+154x^87+291x^88+382x^89+397x^90+502x^91+603x^92+706x^93+912x^94+1056x^95+1120x^96+1240x^97+1245x^98+1314x^99+1161x^100+1072x^101+912x^102+698x^103+516x^104+454x^105+284x^106+266x^107+203x^108+146x^109+133x^110+92x^111+109x^112+36x^113+45x^114+14x^115+31x^116+6x^117+9x^118+3x^120+5x^122+2x^124+2x^126+1x^142 The gray image is a linear code over GF(2) with n=392, k=14 and d=168. This code was found by Heurico 1.16 in 37.4 seconds.