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 1 1 X^2 X X 0 0 0 1 1 X 1 X X X^2 1 X 0 X 0 X^2 1 1 0 0 1 X^2 X X X^2 X 1 1 1 1 X^2 1 X X^2 1 1 X 1 0 1 X 1 1 1 X^2 1 X 1 1 X 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 X^2+X X^2+X 0 X 0 X^2+X X^2 X^2 0 0 X X X^2 X^2+X X X^2 X^2 X^2 X 0 0 X^2+X X^2 0 X^2+X X^2+X 0 X X^2+X X X^2+X X^2+X X X 0 X^2 0 0 X^2 X^2 X^2 X X^2+X 0 0 0 0 X X^2 X^2 X X^2 X X^2 0 X^2 X^2 X^2+X X X^2+X 0 X^2+X X X X^2 X^2 X^2+X X X X^2+X X X X^2 X^2+X X^2 X^2 X X^2 X 0 X X^2+X 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 X^2 0 X^2 X X^2 X^2+X X^2+X X X 0 0 X X^2+X X^2 X 0 0 0 X^2 X 0 X^2 X^2 X 0 X^2+X X^2+X X 0 0 X X^2 X^2+X X 0 X^2+X X X^2 X^2+X X^2+X 0 X^2+X X^2 X^2+X X X^2+X X^2 X 0 0 X^2 X X 0 X^2 X X 0 0 X X^2 X^2+X X^2+X X X X X X^2 X 0 X^2 X^2+X X 0 0 X 0 X^2+X 0 X^2+X 0 X 0 0 0 X X 0 X^2+X X 0 X 0 X X^2+X X^2+X X^2 X^2 X X X^2 X^2 X^2 X X X^2+X X^2 X^2 0 X^2 X^2 X^2+X X^2+X X X^2+X X^2+X X X X X^2 X^2+X X X^2 0 X X^2+X X^2 X^2 X^2+X X X^2 X X^2+X X X^2 0 X X^2 X^2+X X 0 X^2 X X^2+X X^2 X 0 X^2 X^2+X 0 X X^2+X X X^2+X 0 X^2+X X X 0 0 X X^2 X^2 X^2 X^2 X^2+X X^2 X^2 X^2+X 0 0 0 X^2+X X^2+X X X^2+X X^2 X^2+X 0 X X 0 0 0 0 X^2 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 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 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 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 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 0 0 X^2 0 X^2 0 0 0 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 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 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 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 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 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 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 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 generates a code of length 99 over Z2[X]/(X^3) who´s minimum homogenous weight is 86. Homogenous weight enumerator: w(x)=1x^0+135x^86+470x^88+32x^89+579x^90+100x^91+907x^92+288x^93+1175x^94+492x^95+1393x^96+772x^97+1589x^98+792x^99+1657x^100+688x^101+1214x^102+520x^103+1227x^104+248x^105+750x^106+132x^107+502x^108+16x^109+325x^110+12x^111+179x^112+4x^113+97x^114+53x^116+13x^118+8x^120+9x^122+1x^124+2x^126+1x^128+1x^136 The gray image is a linear code over GF(2) with n=396, k=14 and d=172. This code was found by Heurico 1.16 in 39 seconds.