The generator matrix 1 0 0 0 1 1 1 1 X X^2+X X 1 X^2 1 1 0 X^2+X 1 1 1 X^2 1 1 X^2 X 1 1 X 1 X 1 X^2+X 1 1 X^2 0 0 X 1 X 1 X^2+X 1 1 X X^2+X 1 X X 1 1 X 1 1 1 1 X^2+X 1 1 X X^2+X 1 0 X^2+X X X 1 X X^2+X 1 X 0 1 X^2+X 0 X^2+X 0 1 1 X^2 1 1 1 X^2+X 1 1 1 0 1 0 0 X X X^2+X X+1 X^2+X 1 1 X^2+X+1 1 X^2+X+1 X+1 0 1 X^2 1 X^2+X X 1 0 1 1 X^2+X+1 X 1 X^2+1 X^2+X 1 X X^2+X X^2 1 X^2 1 1 0 X^2 1 0 1 X^2 X^2+X 1 X^2+X 1 0 X 1 X^2 0 0 X^2+X X+1 X^2 1 X^2+X+1 X 1 X^2+X+1 X 1 1 1 X+1 X^2+X 1 0 0 1 X^2+1 1 X^2 X^2+X X^2+X 1 X+1 1 X 0 X^2+X+1 X^2+X X^2+X+1 X 0 0 0 1 0 X X^2+X+1 X^2+X+1 X+1 1 X^2+X X+1 X^2+X X^2+1 X^2+1 X^2 1 X^2 X X^2+X 1 1 1 X^2+1 X^2+X+1 X^2+X+1 0 X^2+X X^2 X^2+1 X^2 0 1 X^2+X+1 X+1 X^2+X+1 1 X^2+1 X X^2 1 0 0 X^2+1 X+1 1 X 0 X+1 1 X X^2+X+1 1 X^2+X X+1 1 X X^2+X X^2 X X X X^2+X 1 X^2+X 1 1 X^2 1 X+1 X X X+1 1 0 1 1 0 X^2+X+1 X^2+X 1 0 X X^2+X+1 1 X 1 X^2 0 0 0 1 X+1 X^2+X+1 X X^2+X+1 X^2+X+1 X+1 X^2+X X^2+X 1 0 X^2+X+1 X^2+X X+1 X^2+1 X^2+X X^2+1 X+1 X^2+X+1 X 0 X^2+1 1 X X X^2 1 X X^2 X^2+1 X^2+X X^2+X+1 X+1 X^2+X X^2 1 X 0 1 X^2+X 1 1 X^2+1 X^2 0 X^2+X X^2+X+1 X^2 1 X X^2+X+1 1 0 1 1 1 1 0 1 X^2 X+1 X 0 X^2 X+1 X^2+X+1 X 1 X^2+X X X^2 X+1 X+1 1 X+1 X+1 X^2+X+1 X 0 X^2 X^2 X^2+X X^2+X X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 79. Homogenous weight enumerator: w(x)=1x^0+74x^79+297x^80+498x^81+666x^82+590x^83+570x^84+714x^85+692x^86+636x^87+616x^88+554x^89+412x^90+442x^91+340x^92+310x^93+239x^94+134x^95+159x^96+100x^97+64x^98+28x^99+32x^100+16x^101+7x^102+1x^104 The gray image is a linear code over GF(2) with n=348, k=13 and d=158. This code was found by Heurico 1.16 in 4.72 seconds.