The generator matrix 1 0 0 1 1 1 0 1 X X^2 1 1 X 1 X^2+X X^2 X^2+X 1 1 1 1 X 1 1 0 1 X^2+X X^2+X 1 1 0 1 1 1 X^2+X X^2+X X 1 1 1 1 1 1 1 1 1 X 0 1 1 0 1 X^2 1 0 X^2 1 1 1 X^2 1 X^2+X 1 1 0 1 1 1 1 1 1 X^2 1 1 0 1 1 1 0 1 0 0 1 1 1 X 1 X^2+X 1 X^2+X 1 X+1 X^2 1 1 X^2+1 X^2 X^2+X+1 X 1 0 X+1 1 X 1 X^2+X X+1 X^2+X 0 X^2+1 X^2 X^2+X+1 1 1 X^2 X^2 1 X 1 X^2+1 1 X^2+X 0 X^2+X X^2 X^2+X X^2+X+1 X 1 0 1 X^2+X 1 1 X+1 X+1 X^2+X+1 X 0 X^2+X X^2+1 X+1 1 X X^2+X+1 X^2+X X^2 X^2+1 1 1 X^2+1 X^2+1 1 0 X^2+X X^2+X+1 0 0 1 X+1 X^2+X+1 0 X+1 1 X^2 1 X^2+1 0 1 X 1 X X+1 X X^2+1 X^2+1 X^2+X X X X+1 X+1 1 X^2+X+1 1 0 X+1 1 X^2 X X 1 X^2+X 1 X^2+X X+1 1 X^2+X+1 0 X X^2+X 1 X^2 1 1 X^2 X^2 X^2 1 1 X X^2 1 X+1 X^2 X^2 1 X^2 1 X^2 X+1 X+1 X^2 X^2+1 X^2 X^2+X 1 X^2+X X^2+X+1 X X^2 X X^2+X+1 X^2+1 X 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+388x^72+684x^74+905x^76+620x^78+589x^80+360x^82+260x^84+140x^86+86x^88+52x^90+9x^92+2x^100 The gray image is a linear code over GF(2) with n=312, k=12 and d=144. This code was found by Heurico 1.16 in 29.5 seconds.