The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 1 1 X^2+X 1 1 0 1 1 0 X^2+X 1 1 1 0 1 1 X^2+X 1 1 1 X 0 1 1 0 1 1 X^2+X 1 0 1 1 1 1 1 X^2+X X 1 0 1 X^2+X 1 1 1 1 X^2 1 1 1 1 X 1 1 1 1 X^2 X 1 1 1 X 1 1 1 X^2 X^2+X 1 X^2 X 0 1 1 1 1 1 1 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X X^2+1 1 0 X+1 1 X^2+1 X^2+X 1 X X^2+1 1 1 X+1 0 X^2+X+1 1 0 X^2+1 1 X^2+X 0 X+1 1 1 X^2+1 X^2+X 1 X X+1 1 X^2+1 1 X^2+X X+1 X+1 X^2+X X+1 1 1 X^2+1 1 X 1 X^2+X+1 0 0 X^2 1 X+1 X^2+1 X^2+X+1 X 1 X^2+X X X^2 1 1 1 X^2 X^2+1 X^2+X+1 1 X X+1 0 1 1 X^2+1 X 1 X^2 X X^2+X X+1 X^2+1 1 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 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 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 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 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 77. Homogenous weight enumerator: w(x)=1x^0+12x^77+65x^78+132x^79+147x^80+352x^81+333x^82+508x^83+288x^84+682x^85+511x^86+844x^87+478x^88+868x^89+513x^90+780x^91+256x^92+516x^93+268x^94+256x^95+81x^96+124x^97+67x^98+40x^99+6x^101+16x^102+26x^104+11x^106+3x^110+3x^112+4x^114+1x^118 The gray image is a linear code over GF(2) with n=352, k=13 and d=154. This code was found by Heurico 1.16 in 10.4 seconds.