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 0 1 X^2 1 X^2 1 1 1 1 1 1 X 1 1 X 0 1 1 1 1 0 1 1 X 1 1 0 1 1 X 0 1 1 X 1 X 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^2 X^2 0 X^2 X X^2+X X 0 X^2+X X X^2+X X^2 0 X X^2 X^2 X^2+X X X^2 X X^2 0 X^2+X 0 0 X^2+X X^2 X^2 X 0 X X^2 X 0 0 0 X X^2+X X X^2+X X^2+X X X^2 X X X^2 0 X X^2 X X X^2 0 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 X 0 0 X X X^2 X^2+X X X^2 0 0 X 0 X^2 X X X X^2 X^2+X X^2 X^2+X 0 X^2 X^2+X X^2 X^2+X X^2 0 0 X^2+X X^2+X X 0 X X^2+X X X X X^2 0 X^2+X X X^2 X^2+X 0 X 0 X^2 0 X^2 X X^2+X 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^2+X 0 X X^2+X 0 0 X^2 X X^2+X X^2+X 0 0 0 X^2+X 0 X X^2+X X^2+X X X^2+X X^2 0 X^2+X X X X^2+X X^2 X^2 X^2 0 X^2 0 0 X^2+X X^2 X X X^2 0 X X X^2+X X^2 X^2+X 0 X^2+X 0 X X^2+X X^2 X^2 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 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 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 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 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 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 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 0 X^2 generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+39x^68+50x^69+85x^70+114x^71+117x^72+164x^73+203x^74+216x^75+208x^76+208x^77+145x^78+138x^79+110x^80+62x^81+47x^82+24x^83+26x^84+18x^85+20x^86+16x^87+8x^88+10x^89+10x^90+4x^91+3x^92+1x^94+1x^126 The gray image is a linear code over GF(2) with n=304, k=11 and d=136. This code was found by Heurico 1.16 in 0.634 seconds.