The generator matrix 1 0 0 0 0 1 1 1 0 1 X^2 1 X^2 1 X^2+X 1 0 1 1 X^2 X^2 1 X^2+X 1 X^2+X 1 X^2 1 1 X 1 X 1 1 X^2 1 X^2+X X^2+X X^2+X 1 0 1 1 1 X^2+X 1 1 X^2+X 1 X^2+X 0 X^2+X 1 1 X^2+X 1 0 1 0 X X^2 X 1 1 1 1 1 X^2+X 0 1 X^2 1 0 X^2+X 1 0 X 1 1 1 1 1 1 X^2+X X^2+X 1 1 1 0 1 0 0 0 0 0 X^2 X^2 1 1 1 1 1 1 X+1 X^2+X X^2+X X^2+X 1 1 X^2+X+1 X^2+X X+1 1 X+1 0 X^2+X X^2+1 1 X 1 1 X+1 0 0 X^2 1 0 X^2+X+1 X^2+X X+1 X^2+X X^2 1 X^2+1 X^2+X+1 1 X 1 1 1 X^2+X+1 X+1 1 X 1 X^2 1 1 1 X^2+X X+1 0 X+1 X^2+1 X^2+X 0 X 0 X 1 X^2 X^2+X 1 1 1 X+1 X^2+X 0 X^2 X^2+X+1 0 1 0 X^2+X 0 X^2+X 0 0 1 0 0 X^2 1 X^2+1 1 0 1 X+1 X^2+X+1 X^2+1 0 X 1 X^2+X X^2+X+1 X^2+X 0 X^2+X X^2 1 X^2+1 X^2+1 1 X^2+1 X X^2 X^2+1 1 X^2+X 1 1 X^2+X 1 X^2+X+1 1 X^2+X X^2 0 X+1 X+1 X X+1 X+1 X X^2 X+1 X^2 X+1 X^2+1 1 X^2+X X^2 X^2+1 X^2+X+1 X^2+1 0 X+1 X^2+X X+1 X X^2 X+1 1 1 X 1 1 X^2 1 X^2 X^2+X+1 0 X^2+X 0 0 X+1 X^2+1 0 X^2+X+1 X^2 X X^2 X^2+X+1 0 0 0 0 1 0 X^2+1 1 0 1 X^2 X^2+1 X+1 X^2 X^2+X X^2+1 X^2+X+1 X^2+X 0 X^2+X X+1 X^2+X X^2+X 1 X^2+X 1 X+1 X+1 X^2+X+1 X^2+X X^2 X X^2+X X^2+X+1 X X X^2+1 X^2+X X^2+1 X^2 1 1 X X^2+X+1 X^2+X X^2 X^2 X^2+X+1 X^2+1 X^2 X^2+X X+1 0 X^2+X+1 X+1 X+1 X+1 X+1 0 X 0 X^2 1 X^2 X X 0 X X^2+1 1 X+1 1 X X^2+X 1 X^2+X X^2+X+1 0 X^2+X+1 X^2+X+1 X+1 X^2+X 1 X^2 1 1 X^2+1 X+1 0 0 0 0 0 1 1 X^2 1 1 X^2+1 X^2 1 X+1 0 1 0 X^2+1 X^2+X+1 X X X^2+X+1 X^2+X X^2+X+1 1 X+1 X X^2+X X^2+1 X^2+1 0 X^2+X 0 1 X+1 X^2+X+1 0 X^2+X X^2 X+1 X^2+1 X X^2 X+1 X^2+1 X+1 1 X X^2+X X^2+X 0 X^2 1 0 X^2+X+1 X^2+1 X^2+X+1 0 X^2+X X X^2+X+1 1 X^2+X X^2 X^2+X X^2+X 0 0 1 X^2 1 X^2+X X^2+X+1 X X^2+1 X 1 X X^2 X^2+X X^2+X+1 1 X^2 X^2+X+1 X^2+X+1 X^2+X+1 1 X^2+1 X^2 generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+149x^78+484x^79+951x^80+1230x^81+1665x^82+1670x^83+2092x^84+2104x^85+2654x^86+2186x^87+2704x^88+2338x^89+2431x^90+2162x^91+2176x^92+1606x^93+1364x^94+928x^95+756x^96+428x^97+320x^98+174x^99+104x^100+34x^101+25x^102+10x^103+16x^104+4x^105+2x^107 The gray image is a linear code over GF(2) with n=352, k=15 and d=156. This code was found by Heurico 1.16 in 58.2 seconds.