The generator matrix 1 0 0 1 1 1 0 1 1 1 X X^2 1 X^2 1 X^2+X 1 1 X^2+X 1 X^2+X 1 1 0 1 1 X^2 X^2+X 1 X^2+X 1 1 X 1 1 1 X X^2+X 1 1 1 0 X X^2 X^2 1 1 0 X 1 1 X 1 1 X^2+X 1 1 1 1 1 1 X^2 1 X 1 1 X^2 X^2 1 X^2+X 1 1 1 1 1 X^2+X X^2 1 1 0 1 0 0 1 1 1 X^2 X^2+X+1 X+1 1 1 X X^2+X X^2+1 1 X^2+X+1 X X^2+X X^2+X 1 1 0 1 X X^2+X+1 1 X^2 X^2+X+1 1 X^2+1 0 1 X^2+X X^2+X 0 X 1 0 X X^2+X+1 1 1 X^2+X 1 0 X^2+1 1 1 X 1 1 X^2 X+1 0 X^2+X X^2+X X^2+1 X^2+X X^2 X^2+1 1 X 1 X^2+1 X^2 1 1 X^2 1 0 X^2 1 X^2 X 1 1 X^2+1 0 0 0 1 X+1 X^2+X+1 0 X+1 X X^2+X X^2+X+1 X^2+1 X 1 1 X^2+1 X^2+X+1 X^2 0 1 X+1 0 X 1 X^2 0 X 1 1 1 X 1 0 X^2+X+1 X+1 X^2+X 1 1 X^2 X^2+X+1 X^2+X X+1 X^2+X+1 1 1 X^2+X 1 X^2+X X^2+X+1 1 0 X^2 X^2+X+1 X^2 0 1 X^2+1 X X^2+1 1 X^2+X X^2+X+1 X+1 0 X 0 X^2 X+1 1 X+1 X+1 X 0 1 1 X+1 X^2+1 X X 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 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 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 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 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 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+59x^72+200x^73+307x^74+354x^75+410x^76+434x^77+392x^78+350x^79+285x^80+224x^81+214x^82+192x^83+166x^84+140x^85+92x^86+108x^87+89x^88+16x^89+10x^90+14x^91+12x^92+10x^93+8x^94+6x^95+2x^96+1x^106 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 1.1 seconds.