The generator matrix 1 0 0 0 1 1 1 1 X^2+X 1 1 X^2 0 1 0 1 X X 1 1 1 1 X^2 1 X^2+X 1 0 1 0 1 0 1 1 1 1 X 1 X 0 X^2+X X^2 1 X^2+X 1 1 1 X^2 0 X 1 1 1 1 1 0 X^2 X^2+X 1 1 X^2+X 1 X^2 1 1 1 1 1 1 1 1 X X^2 X 1 X^2 1 0 1 1 1 1 1 0 1 0 0 0 X^2 1 X^2+1 1 X^2 X^2+X+1 1 X^2+X X^2+1 1 X^2+X X 1 X^2+1 X^2+1 1 0 1 X+1 X^2+X X^2 X^2 X+1 1 X^2+X 1 X^2+X+1 X^2+1 0 X^2+X 1 X^2+X X^2 X 1 X^2 X^2+X 1 X X^2+X+1 X^2+X+1 1 X^2 0 X^2+1 X^2+X X^2+X+1 X X 0 1 X X^2+X+1 1 1 X+1 1 X^2+1 X^2+X+1 X^2 X^2+1 X^2 X^2 1 0 X^2+X 1 1 X^2+X+1 0 X^2 1 X+1 0 1 X X^2 0 0 1 0 0 X^2+1 X^2 1 1 X+1 X^2+X+1 1 1 X^2 0 0 1 X^2+X+1 X X^2 X+1 X^2+X+1 X^2+X 1 X X^2+1 1 X+1 X^2+X X^2 X+1 X^2+X X^2+X+1 1 X^2 1 X 1 1 X^2+1 1 X+1 X 1 X^2 1 X^2+X 1 X^2+X X X^2+X+1 X^2+X X X^2+X 1 X^2+X X X+1 X^2+1 X^2+X X^2+X X^2+X+1 X^2+X X X+1 X X^2+X X X^2+1 X 1 0 1 X^2+X+1 1 1 X X^2+1 1 X+1 X^2 X^2 0 0 0 1 1 1 X^2+1 X 1 0 X+1 X^2+X X^2+1 X X+1 X+1 X+1 1 X^2+1 X^2+X 1 X^2+X+1 1 X^2+X 1 X X X+1 X^2 0 X X+1 0 X^2+X X^2+1 0 0 X^2+X X^2 X+1 X^2+1 X X+1 X^2+X+1 X^2+X+1 1 1 1 1 X X X^2+1 X X^2+X+1 X+1 0 1 X+1 0 X^2+1 X+1 X+1 X^2+X+1 X^2+X X^2+1 X 1 X^2+1 0 1 X^2 X^2+1 X^2+X X^2+1 X+1 X+1 X X+1 X^2+X X+1 X 0 0 0 0 0 X 0 0 0 0 X X X X X X 0 0 X^2+X X X^2 X^2 X^2+X 0 X X^2+X X^2 X^2+X X^2 X^2+X X^2+X X^2 X^2 X X^2+X X X X X X^2 X^2 X^2 0 0 0 X X^2+X X^2+X X X^2+X X^2 X 0 X^2+X X^2+X X^2 X X^2 0 X 0 X^2+X X 0 X^2+X X^2+X X X X^2 X^2+X 0 X^2+X X^2 X^2 X^2+X X 0 0 0 X^2 0 X^2+X 0 generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 73. Homogenous weight enumerator: w(x)=1x^0+122x^73+356x^74+564x^75+836x^76+1108x^77+1088x^78+1134x^79+1245x^80+1270x^81+1320x^82+1272x^83+1214x^84+1140x^85+1035x^86+800x^87+582x^88+432x^89+313x^90+212x^91+138x^92+110x^93+37x^94+10x^95+16x^96+8x^97+11x^98+8x^99+2x^101 The gray image is a linear code over GF(2) with n=328, k=14 and d=146. This code was found by Heurico 1.13 in 5.13 seconds.