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 X 1 X X 1 X 1 1 1 1 1 1 1 X 1 1 1 X 1 X 1 1 1 1 1 1 1 1 X 1 1 X 1 X 1 X X X^2 X 1 1 1 X X 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 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 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 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 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 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 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 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 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 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 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 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 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 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 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 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 X^2 X^2 0 X^2 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+142x^76+8x^78+209x^80+60x^82+274x^84+202x^86+1024x^87+361x^88+1024x^89+168x^90+237x^92+60x^94+141x^96+12x^98+100x^100+2x^102+49x^104+15x^108+6x^112+1x^144 The gray image is a linear code over GF(2) with n=352, k=12 and d=152. This code was found by Heurico 1.16 in 5.99 seconds.