The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2 1 1 X 1 1 X 0 1 1 X 1 1 1 X 1 1 X^2 1 1 1 1 X 1 X^2 1 0 1 1 X^2 1 1 1 X^2 1 X^2 1 1 1 1 1 1 1 1 1 X^2 X^2 1 X^2+X X 1 1 X 1 X^2+X 1 1 0 X^2+X X 1 1 1 1 X^2 X^2 0 1 X^2 1 0 0 1 1 0 X^2+X+1 1 X+1 X^2+X 1 X^2 X^2+1 1 X X^2+X+1 1 1 X^2+X+1 X^2+X 1 X^2+1 X X+1 1 0 X^2+1 1 X^2+X X^2+1 X^2 X 1 X+1 1 X 1 X+1 X^2+X+1 1 X+1 0 0 1 X^2 1 X^2+1 X X+1 X^2 X^2+X+1 X X 0 X^2+X 1 1 0 1 1 0 X^2+X+1 1 X^2+1 1 X^2+X+1 X^2+X+1 1 1 1 X^2+X+1 1 X^2+X 1 1 1 1 1 1 X+1 X 0 0 X 0 X^2+X 0 X^2 X^2 X X^2+X 0 X^2+X X^2+X X^2 0 X^2+X X^2+X X^2+X X X^2 0 X X^2 X^2+X X^2+X X^2 X^2 X^2+X 0 X^2 X^2+X 0 X^2+X X 0 X X^2 X X^2 X^2+X X^2 X X 0 X^2+X X X^2 0 X^2 X^2+X X X^2 X X X X^2 X^2 X^2 X 0 X^2+X X X^2 0 X X^2 X^2 X X X^2 X^2 0 X^2 X X X X 0 X^2+X 0 0 0 X 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2+X X^2+X X X X^2+X X X^2+X X^2+X X X^2+X X^2+X X^2+X X^2+X 0 X^2 X^2+X X^2+X X^2 0 0 X X^2 X^2+X X X^2+X X^2+X X X^2+X X X^2 X^2 X^2 0 0 X^2 X^2 X^2+X 0 X^2+X X^2 0 X 0 0 X^2 X X^2+X X^2+X X 0 X^2 X^2+X X^2 X 0 X^2 X^2+X 0 0 X^2+X X^2+X X^2 X^2 X^2+X X 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 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 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 X^2 0 generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+187x^72+136x^73+365x^74+268x^75+410x^76+244x^77+393x^78+232x^79+329x^80+272x^81+397x^82+252x^83+293x^84+116x^85+87x^86+16x^87+30x^88+26x^90+15x^92+8x^94+8x^96+4x^98+5x^100+1x^104+1x^108 The gray image is a linear code over GF(2) with n=316, k=12 and d=144. This code was found by Heurico 1.16 in 1.38 seconds.