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 0 X^2 X X^2 X 1 1 X^2 X 0 X X^2 1 1 0 X 1 0 X X^2 1 1 1 X 1 1 1 X^2 X X X 0 1 1 1 X^2 X X^2 1 0 1 0 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 X^2+X X^2+X 0 X 0 X^2+X 0 X^2 X^2 X^2 X X X X 0 X^2 X 0 0 X^2+X X 0 X^2 0 X^2+X X^2 X^2+X X X X^2 0 X X 0 X^2 X^2 0 X^2 X^2 X X^2+X 0 X X^2+X X X^2 X^2+X X X^2 X^2 X X^2+X X 0 X^2+X X 0 X^2 X^2+X X 0 0 X^2+X X 0 X X^2+X X^2 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^2+X X X X^2 X^2+X 0 0 X^2 X^2 0 X^2+X X X^2+X X X^2+X X^2+X X^2 0 X X X X X X X X X^2+X X^2+X X X^2+X 0 X^2+X X X^2+X X^2+X X X 0 X 0 X^2 X^2 0 X 0 X^2+X 0 0 0 X X^2+X X^2+X X 0 X X X^2+X X^2+X X^2 X^2+X X X X^2+X X^2 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 X^2 0 0 X^2 X^2+X X^2 X^2 0 0 0 X X^2 X^2 X^2+X X X X^2+X X^2 X^2+X X^2+X X^2+X X X^2+X 0 X^2 X^2+X X^2+X X 0 X X 0 X^2+X 0 X X^2+X X^2+X X^2 X^2 X^2+X X^2+X X^2+X X^2 0 X^2 X^2+X X^2+X 0 X^2 X^2+X X^2 X^2 X^2+X X^2 0 X^2 X^2 0 X^2+X X^2 X^2 X X^2+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 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 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 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 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 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 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 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 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 0 0 0 0 X^2 X^2 0 X^2 0 0 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 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 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 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 76. Homogenous weight enumerator: w(x)=1x^0+250x^76+4x^77+444x^78+28x^79+771x^80+128x^81+966x^82+376x^83+1341x^84+648x^85+1540x^86+872x^87+1772x^88+896x^89+1640x^90+608x^91+1335x^92+340x^93+852x^94+156x^95+575x^96+32x^97+342x^98+8x^99+278x^100+92x^102+60x^104+12x^106+10x^108+5x^112+1x^116+1x^124 The gray image is a linear code over GF(2) with n=352, k=14 and d=152. This code was found by Heurico 1.16 in 33.3 seconds.