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 1 1 X^2 X X 0 1 X X^2 X^2 1 0 X 1 1 0 1 X^2 X 1 1 X^2 1 X^2 X^2 1 1 X X X 0 1 X 0 1 1 1 X^2 X 1 1 1 0 1 X X 0 1 1 1 X^2 X 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 X X X X^2+X X^2+X X^2 X^2+X X^2 X X X X X 0 X^2+X X X X^2+X X X^2 X X 0 X X X^2+X 0 X^2 X^2 X^2+X X X^2 X^2 X 0 X^2 X X 0 X^2 0 0 X^2 X X^2 0 0 X X X X^2+X 0 X X X X^2+X 0 X^2 X 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 X^2 0 0 X^2 0 X^2 X^2+X 0 0 0 X^2 X 0 X X^2+X X^2 X X^2 X X^2+X X 0 X X X^2 X X^2 X X 0 0 X X^2+X 0 X X^2 X X^2 X^2+X X^2+X X^2 X^2+X X X^2+X X X^2 0 X^2 X X^2+X 0 X 0 X X X^2 X^2 X 0 0 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 X X^2+X X X^2+X X^2 X^2 0 0 X^2 X X 0 0 X^2 X X X^2 0 X^2+X X X^2+X 0 X^2 0 X X^2+X X^2+X X X^2+X X^2 X^2+X 0 X^2+X X^2 X^2 X X^2 0 0 X X X X^2+X X X^2+X X^2+X X^2+X X X^2+X X^2+X 0 X^2+X X^2+X X^2+X X^2 X X^2 X X 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 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 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 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 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 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 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 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 X^2 0 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 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 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 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 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 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 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 0 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 82. Homogenous weight enumerator: w(x)=1x^0+31x^82+52x^83+180x^84+170x^85+265x^86+360x^87+432x^88+524x^89+659x^90+752x^91+846x^92+1066x^93+1141x^94+1188x^95+1204x^96+1240x^97+1090x^98+1112x^99+901x^100+702x^101+569x^102+416x^103+348x^104+300x^105+236x^106+160x^107+140x^108+78x^109+82x^110+52x^111+29x^112+16x^113+15x^114+4x^115+13x^116+5x^118+2x^120+1x^122+1x^126+1x^134 The gray image is a linear code over GF(2) with n=384, k=14 and d=164. This code was found by Heurico 1.16 in 36 seconds.