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 X 0 1 1 1 1 1 1 1 1 1 X 1 X 1 X 1 0 1 1 1 0 1 1 1 X 1 0 1 X^2 1 X 1 1 1 1 0 X 0 0 0 X X^2+X X X^2 X^2 X 0 0 X X X^2+X 0 0 X^2+X X X^2 X X^2+X X X^2 0 X^2 X^2 X^2+X 0 X X^2+X X X^2+X X^2+X X 0 X^2 X^2+X X 0 0 X^2 0 X^2 X^2 X 0 X 0 X^2+X X^2 X^2+X X^2 X^2+X X 0 X^2 X^2 X 0 X 0 X X^2 0 X X X^2 0 X 0 X^2 X^2 0 0 X 0 X X X 0 X^2 0 X^2+X X X^2+X 0 X^2+X 0 X^2 X^2+X X^2 X^2+X 0 X^2 X 0 X^2+X X^2+X X X^2 X X^2 0 X^2+X X X 0 X^2 0 X^2+X X^2 X^2 0 X X^2+X 0 0 X^2+X X^2 X^2+X X 0 0 X^2+X X^2+X X X^2 X^2 X^2 X^2+X X^2+X X^2+X X X^2 X X X^2 X X^2+X 0 0 X^2+X 0 0 0 0 0 0 0 X X 0 X X^2+X 0 X X^2 X X^2 X^2+X X 0 X^2 X X 0 X^2+X X^2 X^2+X X^2+X 0 0 X^2+X X X 0 0 0 0 0 X^2 X^2 X^2 X X^2 X^2 X 0 X^2+X X^2+X X^2 X^2+X X 0 X^2 X^2+X X^2+X X^2+X 0 X^2 0 X X^2+X 0 X 0 X^2+X X^2+X X^2 X X^2 0 0 X^2+X X^2 X X X^2 0 X 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 0 0 0 X^2 0 X^2 X^2 X^2 X^2 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 0 X^2 0 X^2 0 0 0 0 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 X^2 X^2 0 X^2 X^2 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 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 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 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+35x^66+52x^67+72x^68+108x^69+88x^70+290x^71+55x^72+328x^73+52x^74+430x^75+58x^76+152x^77+39x^78+88x^79+47x^80+40x^81+33x^82+28x^83+12x^84+12x^85+8x^86+6x^87+9x^88+2x^91+2x^92+1x^126 The gray image is a linear code over GF(2) with n=296, k=11 and d=132. This code was found by Heurico 1.16 in 0.597 seconds.