The generator matrix 1 0 1 1 1 X^2 1 1 0 0 1 1 1 0 1 1 X^2 1 1 1 X^2 1 1 0 1 X^2 1 1 X 1 X^2 1 1 1 1 1 0 1 1 1 X 1 1 1 1 X^2+X 1 1 1 1 X^2 X^2+X 0 1 1 X^2+X X 1 1 X^2+X 1 X 1 X 1 X 1 1 X^2+X X^2 1 1 1 1 X^2 1 1 X 1 1 1 X 1 1 X X^2+X 0 1 0 1 1 0 1 1 X^2 X+1 1 1 X^2 X^2+X+1 X^2 1 X^2+1 X^2 1 X^2+X+1 X^2+X 1 1 X^2 X+1 1 X^2 1 X^2+X+1 X^2+X 1 1 1 X^2+1 X^2+X X^2+X+1 0 X 1 X 1 1 1 X+1 X+1 X^2+1 0 1 X X^2+X+1 0 X^2+X 1 1 1 0 1 1 1 X^2 X^2+X 1 X 1 X^2+1 1 0 1 X^2+1 X 1 1 X+1 X^2 1 X^2+X+1 1 1 X^2+X X X X^2+X X^2+X+1 X 1 0 1 1 1 0 0 0 X 0 0 0 0 X^2 X^2+X X X^2+X X^2+X X^2+X X^2 0 X^2+X X X^2+X 0 X^2+X X^2 X X^2 X^2+X X^2 X^2 X^2 X^2+X X^2 X X^2+X X^2+X X^2+X X^2 X X 0 X^2 X^2 0 X^2 0 0 X X^2 X 0 X^2+X X X^2+X X^2 X X X X 0 0 X^2 X^2+X X^2 0 X 0 0 X^2 X X^2 X^2+X X^2+X X^2+X X^2+X X^2+X 0 X^2+X X^2 X^2 X^2 X X 0 X^2 X^2+X 0 X X^2 0 X 0 0 0 0 X 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2+X X X^2+X X^2+X X X^2+X X^2+X X X X X^2+X X^2+X X 0 0 X^2+X 0 0 X^2 0 X X^2 X X^2+X X X^2 X^2+X 0 X X X^2 X^2+X X^2+X X^2 X^2+X X X^2+X 0 0 0 X^2+X X X^2 X X^2 X 0 0 X^2+X 0 0 X X^2+X X^2 0 X^2 X X^2 X^2+X X^2+X X X^2+X 0 X X^2+X X^2+X X X^2+X X^2+X X X^2 X X X^2 0 0 0 0 0 X X^2+X X^2+X X^2 X 0 0 X^2+X X X X X^2+X X^2 X X X^2 0 X^2 X^2 X X^2+X X X 0 0 X X^2 0 X X 0 X X 0 0 X^2+X X^2 X X^2 X X^2 0 X X^2 X 0 X^2 X^2+X X^2 X^2 X^2+X X 0 0 X 0 0 X^2+X X^2 X^2+X 0 X X^2 X^2+X 0 0 X^2 X^2 X^2 X^2+X 0 X^2+X X^2+X X^2 X 0 X^2+X X 0 X^2+X X^2+X X^2 X^2+X X^2 generates a code of length 88 over Z2[X]/(X^3) who�s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+60x^80+122x^81+196x^82+338x^83+348x^84+328x^85+314x^86+252x^87+311x^88+324x^89+295x^90+306x^91+257x^92+206x^93+159x^94+104x^95+51x^96+28x^97+14x^98+18x^99+15x^100+10x^101+8x^102+4x^103+12x^104+6x^105+2x^106+2x^107+2x^110+1x^112+1x^114+1x^118 The gray image is a linear code over GF(2) with n=352, k=12 and d=160. This code was found by Heurico 1.16 in 1.52 seconds.