The generator matrix 1 0 0 0 1 1 1 1 X^2+X 1 1 1 X^2+X X X^2 X^2+X 0 X 1 0 1 1 1 1 X^2+X 1 X^2 1 1 X X X^2+X 1 1 1 X^2 0 0 X^2+X 1 1 1 1 X^2+X X^2+X 1 X^2 X 1 1 0 1 1 0 1 X^2+X X 0 X 1 1 1 1 1 X X^2 1 1 1 0 1 1 1 0 1 X^2+X 0 X^2+X 1 1 1 X^2 X^2 X^2+X X^2 1 1 0 0 1 0 0 0 X^2 1 X^2+1 1 X^2 X^2+X+1 X+1 1 1 0 1 X^2 X^2 X^2+X+1 1 X^2 1 X^2+X X^2+X+1 X^2+X X 1 X^2+X X^2+1 X^2 1 1 X^2 X^2 X^2 X^2+X 1 1 1 X X^2+1 X 1 1 X^2+X X^2+X+1 X X^2 X^2+1 X^2 1 X+1 X^2+1 1 X^2 X^2+X 0 1 1 1 X^2+X+1 X+1 X^2+X+1 X^2+X 1 1 1 X^2 X 1 X^2+X+1 0 X 1 0 1 X X 0 X^2 X+1 X^2+X X 1 1 X+1 1 1 0 0 1 0 0 X^2+1 X^2 1 1 X+1 X^2+X+1 X^2 X+1 X 1 1 1 X^2+X 1 X^2+X 0 X 0 X^2 1 1 X^2+X 1 1 X^2+X 1 X^2+X+1 X+1 1 X 1 0 X^2+X X^2+X+1 X+1 X^2+X X 0 X^2+X 0 X^2+X+1 1 1 X X^2+1 X^2+X X+1 X^2+1 X+1 X^2+X X^2 1 X^2+1 0 X^2 X^2+X X X^2+X X^2+X X^2+X X^2+1 1 X+1 X^2 0 X^2 X X^2+X+1 1 X^2+X X^2+1 X^2+X 1 X X^2+1 1 1 1 X^2+1 X^2+X 1 X X^2+1 0 0 0 1 1 1 X^2+1 X 1 0 X+1 0 X 1 X+1 X^2+X X+1 1 X^2+X 0 X^2+X 1 X^2+X+1 X^2 0 0 1 X^2+X+1 X^2+1 1 X+1 X X^2+X X+1 X X^2 X^2+1 X 1 X^2+1 1 X^2+X+1 X 0 1 X^2 X^2+X+1 X^2 X X^2+X+1 X^2 X^2+X+1 X+1 X^2 X^2 1 1 X^2 1 X^2+X+1 1 X^2+X X^2+1 X^2+1 X^2+X X^2+X X^2+1 X+1 X^2 X^2+1 0 X^2+X X^2+X+1 X+1 X^2+X+1 X^2+1 1 1 1 X^2+X X^2+X X^2+X+1 X+1 X^2 1 X^2 X^2+X 0 0 0 0 0 X 0 0 0 0 X X X X X X X X^2 X^2+X X X X^2+X X^2+X 0 X^2 X X^2+X 0 X^2+X X^2 X^2 X^2 0 0 X^2+X X^2 0 X X^2+X X^2+X X^2 X^2 X^2 X^2 0 X 0 X X X 0 0 X^2 X^2+X X^2 0 X^2+X 0 X^2 0 X^2+X X^2+X X^2+X X X^2+X X X^2 X^2+X X^2+X X^2+X X^2+X X^2+X X 0 0 0 X X^2+X X^2 X^2 X X 0 X^2 0 X^2+X X^2+X 0 X^2 generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 79. Homogenous weight enumerator: w(x)=1x^0+216x^79+378x^80+728x^81+712x^82+1070x^83+931x^84+1272x^85+1108x^86+1496x^87+1173x^88+1352x^89+941x^90+1178x^91+910x^92+936x^93+485x^94+536x^95+321x^96+270x^97+121x^98+106x^99+59x^100+44x^101+23x^102+4x^103+3x^104+6x^105+2x^106+2x^115 The gray image is a linear code over GF(2) with n=352, k=14 and d=158. This code was found by Heurico 1.13 in 5.58 seconds.