The generator matrix 1 0 1 1 1 0 1 1 X 1 X^2+X 1 1 1 0 1 1 X^2 X 1 0 1 X 1 1 1 X^2 X^2 1 X 1 X^2 1 1 1 X^2 0 X X X^2 X^2 1 0 1 1 0 X+1 1 X X^2+X+1 1 X^2+X 1 X^2+1 0 X+1 1 X^2 X^2+X+1 1 1 X 1 X^2+1 1 X+1 0 1 1 1 X^2+X+1 1 X^2+1 X X^2 X X^2+1 X 1 0 X^2+X 1 1 0 0 0 X X^2+X 0 X^2+X X X^2+X X 0 X^2 0 X^2 0 0 X X^2+X X^2+X X X 0 0 X X^2 0 X^2+X X X^2+X X^2+X X^2+X 0 X X^2+X X^2+X X X 0 X X 0 X X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 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 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 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 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 generates a code of length 42 over Z2[X]/(X^3) who´s minimum homogenous weight is 32. Homogenous weight enumerator: w(x)=1x^0+38x^32+34x^33+147x^34+244x^35+351x^36+714x^37+695x^38+1618x^39+1200x^40+2500x^41+1368x^42+2544x^43+1056x^44+1636x^45+750x^46+668x^47+371x^48+218x^49+99x^50+44x^51+47x^52+18x^53+11x^54+2x^55+6x^56+2x^58+2x^60 The gray image is a linear code over GF(2) with n=168, k=14 and d=64. This code was found by Heurico 1.16 in 7.63 seconds.