The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 1 X 1 0 1 1 X 1 0 1 1 1 X 0 1 1 X 0 X 1 0 0 0 X 1 X 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2+X X X^2 X^2+X X^2+X 0 X X^2+X X^2+X X^2+X 0 X X^2+X 0 X^2+X X^2+X X 0 X X^2+X X X^2+X 0 X X X 0 X^2+X X^2+X X^2+X 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 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 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 generates a code of length 42 over Z2[X]/(X^3) who´s minimum homogenous weight is 30. Homogenous weight enumerator: w(x)=1x^0+65x^30+10x^31+142x^32+50x^33+228x^34+192x^35+432x^36+594x^37+871x^38+1294x^39+1477x^40+1940x^41+1749x^42+1968x^43+1487x^44+1316x^45+916x^46+582x^47+418x^48+186x^49+206x^50+48x^51+110x^52+10x^53+51x^54+2x^55+25x^56+9x^58+3x^60+1x^62+1x^64 The gray image is a linear code over GF(2) with n=168, k=14 and d=60. This code was found by Heurico 1.16 in 12 seconds.