The generator matrix 1 0 1 1 1 X^2 1 1 0 0 1 1 1 0 1 1 X^2 1 1 1 X^2 1 1 0 1 X^2+X 1 0 1 1 X^2+X 1 1 1 X^2+X 1 1 1 1 1 1 X X^2+X 1 X^2+X 1 X^2+X X^2 X 1 X^2+X 1 1 1 1 1 X^2 1 X X^2+X 1 1 0 1 1 1 X^2+X 1 0 1 1 1 1 X^2+X 0 1 X^2 1 1 1 X^2 1 X 1 X 1 0 1 1 0 1 1 X^2 X+1 1 1 X^2 X^2+X+1 X^2 1 X^2+1 X^2 1 X^2+X+1 X^2+X 1 1 X^2 X+1 1 X^2 1 X^2+1 1 X^2+X X+1 1 X+1 X X^2+X 1 X^2+X+1 1 0 X+1 X^2+X X+1 1 1 0 1 X^2+1 1 1 1 X^2+1 1 0 1 X^2+X X^2 X+1 1 X^2+X 1 1 X X 1 X^2+X+1 X+1 X^2+X 1 X+1 1 X+1 X^2 1 X^2+X 1 X X^2+X 1 X^2+X+1 1 X^2+1 X^2 X^2+1 1 0 X^2 X^2 0 0 X 0 0 0 0 X^2 X^2+X X X^2+X X^2+X X^2+X X^2 0 X^2+X X X^2+X 0 X^2+X X^2 X X^2 X^2+X X^2 0 X^2 X^2+X X^2+X X^2 X^2+X X X X^2 X^2+X X^2+X X^2 X X^2 X^2+X X^2+X 0 X^2+X X^2+X 0 X^2 X^2+X X 0 X^2 X^2 X^2 X^2+X X^2+X 0 0 X 0 X 0 X X^2+X X^2 0 X^2 X^2 X X^2+X X^2 0 X^2 0 X^2 X X X^2 X^2+X X 0 X^2 X X^2+X X X^2 X^2+X 0 0 0 0 X 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2+X X X^2+X X^2+X X X^2+X X^2+X X X X X^2+X X^2+X X^2 0 0 0 X^2+X X X X^2+X 0 X^2 X 0 X^2 X X^2+X X^2 X^2+X 0 0 X X^2+X X^2 X^2+X 0 X^2 X X^2 X^2+X X^2+X X^2 X^2+X X^2+X X^2+X 0 X^2 X^2 X^2 0 0 X^2 X^2+X X^2 0 X^2 X^2+X X 0 X^2 X^2+X X 0 X^2 X X^2+X X X^2+X X^2 0 X^2 X^2+X 0 0 0 0 0 X X^2+X X^2+X X^2 X 0 0 X^2+X X X X X^2+X X^2 X X X^2 0 X^2 X^2 X X^2+X X^2 X^2 X^2+X X X 0 0 X X X^2 X^2+X X^2+X 0 X X^2+X X^2 X^2 X X^2+X 0 0 X^2+X X X^2+X 0 X^2+X X^2 X^2+X 0 X^2 X^2 0 0 X^2 X^2+X X^2 0 X^2 X^2 X^2+X 0 0 X^2+X X^2 X^2+X X^2 X^2+X X^2 X^2+X X^2 0 0 X^2 X^2+X X^2+X X^2 X^2 X^2+X X X^2+X X^2+X generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+52x^78+112x^79+265x^80+250x^81+396x^82+234x^83+426x^84+222x^85+366x^86+218x^87+436x^88+184x^89+300x^90+164x^91+208x^92+88x^93+46x^94+26x^95+31x^96+14x^97+8x^98+8x^99+4x^100+10x^101+14x^102+4x^103+2x^104+2x^107+2x^108+2x^110+1x^112 The gray image is a linear code over GF(2) with n=344, k=12 and d=156. This code was found by Heurico 1.16 in 1.46 seconds.