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 X X^2 X 0 X 1 0 X 0 X 1 X 1 X 1 1 1 1 1 0 X^2 X 1 0 1 1 1 X 1 1 X^2 1 0 0 1 0 0 1 X X^2 X^2 1 X^2 1 0 1 1 1 1 X X 0 1 1 1 X X^2 1 1 1 1 0 X 0 X 0 0 X X^2+X 0 0 X X^2+X X^2 0 X^2+X X^2 X^2+X X^2 X X^2+X X X^2 X^2 X^2+X X^2 X^2+X X 0 X X X X^2 X X 0 0 0 X^2 X X X^2+X X X^2+X X X 0 0 X^2+X X X X^2 X X^2 0 0 X 0 X X X^2 X X X^2 X^2 X^2+X X^2 0 X^2+X X X^2 X^2 X^2 X X X X^2+X X^2+X X^2 0 0 X 0 X X X^2 X^2 0 0 X^2+X X X^2 0 X X X X^2+X X^2 0 0 0 0 X X 0 X^2+X X 0 0 X^2+X X 0 X X^2 X X^2 0 X^2+X X 0 X^2+X X X^2 X X^2+X 0 X^2 0 X^2 X X^2 X X^2+X 0 X^2 0 X 0 X X^2+X X^2 0 0 X^2 X^2 X^2+X X X^2 0 X X X X X^2 0 X^2 0 0 X^2+X X^2+X 0 0 X 0 X^2+X X X X^2 X X^2+X X X 0 X^2+X X^2+X 0 X X X 0 X^2 0 X^2+X X^2+X X^2+X X^2 X^2 X^2+X 0 X^2 0 X^2+X X 0 X X^2+X X^2+X 0 0 0 0 0 X^2 0 0 0 0 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 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 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 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 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 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 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 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 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 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 generates a code of length 99 over Z2[X]/(X^3) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+47x^84+180x^86+373x^88+56x^89+546x^90+260x^91+662x^92+540x^93+698x^94+996x^95+815x^96+1444x^97+886x^98+1576x^99+799x^100+1464x^101+779x^102+1032x^103+720x^104+544x^105+600x^106+212x^107+422x^108+44x^109+298x^110+20x^111+184x^112+4x^113+75x^114+48x^116+27x^118+16x^120+4x^122+6x^124+2x^126+2x^128+1x^130+1x^136 The gray image is a linear code over GF(2) with n=396, k=14 and d=168. This code was found by Heurico 1.16 in 37.9 seconds.