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 X 0 X X^2 X^2 X X 0 1 1 0 X X^2 1 1 X 1 1 1 1 0 1 X 1 1 1 X 1 1 1 1 X X 1 1 X 1 0 0 1 1 X 1 1 1 X X^2 1 1 1 1 1 X 1 X X^2 0 X 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 0 X X^2+X X^2 X^2+X X^2+X 0 X^2+X X^2 X^2+X 0 X^2+X X X X X X X^2 X^2 X^2 X^2+X X^2 X X X X^2+X X^2 0 0 X X^2 X^2 X X^2+X X X^2 X^2 0 0 X^2+X X 0 X X^2 X^2+X 0 0 0 0 X X X 0 X 0 X^2 X^2+X X X^2+X 0 X^2+X X^2 X X^2+X X X^2+X X X X X^2 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 0 X^2 0 X^2+X X^2+X X X^2+X X^2 X^2 X^2+X X^2 X^2 0 X^2+X X^2+X X^2+X X^2+X X X 0 X^2 X X^2+X X X^2 X X X^2 X^2 X 0 X X X^2 X X X^2 X^2+X X^2+X X X^2 X^2+X X^2 X^2+X X^2 0 X^2+X X X 0 X^2 X^2+X X X^2 0 X^2 X^2 X^2+X X X^2+X X^2 X^2 X^2+X X^2 X^2 0 X^2+X X^2 X X 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 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 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 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 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 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 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 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 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 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 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 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 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 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 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 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 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 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 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 0 0 X^2 0 X^2 0 X^2 0 generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 82. Homogenous weight enumerator: w(x)=1x^0+22x^82+40x^83+116x^84+122x^85+246x^86+196x^87+327x^88+342x^89+490x^90+614x^91+773x^92+912x^93+1005x^94+1200x^95+1167x^96+1380x^97+1196x^98+1226x^99+968x^100+866x^101+723x^102+572x^103+505x^104+342x^105+260x^106+194x^107+154x^108+116x^109+96x^110+48x^111+55x^112+16x^113+44x^114+6x^115+20x^116+9x^118+8x^120+3x^122+1x^124+1x^126+1x^128+1x^138 The gray image is a linear code over GF(2) with n=388, k=14 and d=164. This code was found by Heurico 1.16 in 37.7 seconds.