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 X 0 X 0 X 0 1 1 X 0 1 1 X 0 1 1 0 X 1 1 X 1 1 0 X X 1 1 1 1 X 1 1 0 0 1 X 1 X 1 1 X 1 X 0 X 1 1 1 1 1 1 1 1 X X 1 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2+X X^2 0 X^2+X X X^2 X^2+X X^2+X 0 X 0 X^2 0 0 X^2+X X^2+X X X 0 X^2 X^2+X X^2+X X X^2+X X X^2+X X 0 0 X^2+X X X^2+X X^2+X X^2+X X 0 X X X^2+X X^2+X X^2 X^2+X X 0 X X^2+X X^2+X X^2+X 0 X^2 X X^2+X 0 X^2 X X 0 X X^2+X X^2+X X^2+X X^2+X 0 X^2 X^2+X X X 0 X^2 X^2+X X^2 0 X^2 0 X X^2+X 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 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 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 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 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 0 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 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 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 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 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 X^2 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 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 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 0 0 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 X^2 0 X^2 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 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 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 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 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 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 0 generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 76. Homogenous weight enumerator: w(x)=1x^0+120x^76+48x^78+447x^80+4x^81+400x^82+40x^83+881x^84+180x^85+1006x^86+480x^87+1637x^88+840x^89+1608x^90+1008x^91+1847x^92+840x^93+1302x^94+480x^95+1306x^96+180x^97+608x^98+40x^99+581x^100+4x^101+138x^102+224x^104+8x^106+77x^108+2x^110+29x^112+14x^116+3x^120+1x^128 The gray image is a linear code over GF(2) with n=364, k=14 and d=152. This code was found by Heurico 1.16 in 36.8 seconds.