The generator matrix 1 0 0 0 0 1 1 1 0 1 X^2 1 X^2 1 X^2+X 1 0 1 1 X 1 1 X 1 0 0 1 1 1 1 X^2+X X^2 X^2+X 1 1 1 1 X 1 X^2+X X^2 X^2 0 X^2+X X 1 1 1 X^2 1 X 1 X 1 1 X^2+X 1 X X^2+X 1 X^2 1 0 0 1 0 1 1 X^2+X 1 1 1 X^2+X X X^2+X 1 0 0 1 0 1 0 0 0 0 0 X^2 X^2 1 1 1 1 1 1 X+1 X^2+X X^2+X+1 X^2+X X X^2 X^2+X+1 1 X^2+1 1 1 X^2 X X^2+X+1 X^2+X+1 0 1 X^2+X X 0 X^2+X+1 X^2+1 1 X X^2 X 1 1 X 1 X^2+X X^2+X 1 1 X^2+X+1 X^2 X^2+X+1 X X^2+X+1 X^2+1 0 X^2 X^2 1 X^2+X 1 X^2+X 1 X^2 1 0 X^2+X X^2 0 1 X+1 X^2+1 X 1 1 X^2+X 1 0 0 0 0 1 0 0 X^2 1 X^2+1 1 0 1 X+1 X^2+X+1 X^2+1 0 X 1 X X^2+X+1 1 1 0 X X^2+1 X^2+X+1 1 X X^2+X 0 X^2+X+1 X^2 0 1 1 X^2+X 1 X^2+X+1 X^2+X 0 X^2 1 X^2+X+1 X^2+X X X X+1 X+1 X+1 X^2+1 X^2+X+1 1 X^2 X X^2 X^2+X 1 0 X^2 X^2+X X^2+1 1 X^2 X+1 1 X^2 1 1 X^2+X+1 1 X^2+X X+1 X^2 X^2 0 X^2+X 0 X 0 0 0 0 0 1 0 X^2+1 1 0 1 X^2 X^2+1 X+1 X^2 X^2+X X^2+1 X^2+X+1 X^2+X 1 0 X^2+X+1 X+1 X^2 X+1 X^2+1 0 X+1 1 X^2+X X^2+X X^2 1 X 0 X^2+X X^2+X+1 0 X+1 X^2+X 1 1 X+1 X^2+1 X^2+X+1 X^2+X X^2+X+1 X^2 X^2+1 0 X X^2+1 1 X^2+X 1 X^2+X+1 1 0 1 1 X+1 X^2 X^2+X X^2+X+1 X^2+X X^2+X X+1 X+1 X^2+X X^2+X X X+1 X^2+X 0 X X+1 X X^2+1 X^2+X 1 X^2 0 0 0 0 1 1 X^2 1 1 X^2+1 X^2 1 X+1 0 1 0 X^2+1 X+1 X^2+X X^2+X X^2+X+1 X^2+X 0 X^2+X X X+1 X 1 X^2+1 1 X+1 1 X^2+X+1 X^2+X+1 X 0 X^2 X^2+X X+1 1 1 0 X^2+X 1 X 0 X^2+X+1 X+1 X X^2+1 X+1 X^2+X+1 1 X^2 X^2 X^2+1 X^2 X 1 X^2+1 X^2+1 X^2+X+1 X^2+1 0 0 0 1 1 1 X^2+X+1 X^2 X+1 1 X+1 X^2+X+1 X^2 1 X^2+X+1 X^2 generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 69. Homogenous weight enumerator: w(x)=1x^0+88x^69+458x^70+664x^71+1190x^72+1524x^73+1910x^74+1784x^75+2423x^76+2186x^77+2872x^78+2696x^79+2713x^80+2580x^81+2334x^82+1864x^83+1875x^84+1150x^85+1024x^86+574x^87+445x^88+168x^89+100x^90+60x^91+50x^92+12x^93+6x^94+6x^95+7x^96+4x^97 The gray image is a linear code over GF(2) with n=316, k=15 and d=138. This code was found by Heurico 1.16 in 51.7 seconds.