The generator matrix 1 0 0 0 0 1 1 1 0 1 X^2 1 1 1 1 X X^2+X 1 1 X^2 1 X^2+X X^2 X 1 1 X 1 1 X X 1 1 X^2 X^2 X^2 1 1 1 1 X^2 1 1 1 0 0 X^2+X X^2+X 0 0 1 X X 1 1 1 X 1 1 X 0 1 X^2 X^2+X 1 1 0 1 0 0 0 0 X+1 X X^2 X+1 1 X^2 X^2+1 X+1 X^2+X+1 1 1 X^2+1 X^2 1 X^2 1 X X X+1 X^2+1 1 X^2 X^2+X X 1 X X^2+1 1 1 1 1 1 X^2+X+1 1 1 1 0 X+1 X^2+X 1 X 1 X 1 1 0 X 0 0 X^2+X+1 0 0 0 1 1 1 X^2 1 0 0 0 0 1 0 0 0 1 X+1 1 X^2+1 X^2 X^2+1 X^2+X X^2+X+1 X^2+X 1 X^2+X+1 X^2+X+1 0 0 X^2+X 0 1 1 X X^2 X^2+1 X^2+X+1 X^2+1 X X^2+1 X^2 1 X 0 1 X+1 X+1 X X^2+X X^2+1 X X^2 X^2+X+1 1 X+1 0 X^2+X 1 X+1 X^2 1 1 X^2+X+1 X+1 X X^2 0 X^2+X X^2+1 X+1 X^2+1 X X+1 0 0 0 0 0 1 0 1 X^2 X^2+1 1 X+1 X^2+1 X^2+X X^2 X^2+1 X^2+X+1 X^2+X+1 0 X^2+X X^2+X+1 X 0 X+1 X^2+1 0 X X+1 X X^2+1 X^2+X 1 X+1 0 X X^2+X+1 X X^2 X X+1 0 0 X X^2+1 X+1 X^2+X+1 1 X^2+X+1 1 X^2+X X X^2 0 X^2 X^2+X+1 0 X X+1 X^2+X 1 X^2 1 1 X^2+X X^2 1 X^2 0 0 0 0 0 1 1 X^2+1 X X+1 X^2+1 X^2+X X^2+1 0 X^2 X^2+X+1 1 X^2 X 0 X+1 X+1 1 X^2 X^2+X+1 X^2+1 X^2 X^2+1 X+1 0 X+1 X^2+X X X^2+X+1 X^2+1 X+1 X X X^2 X^2 X+1 X^2+1 X^2 X X+1 X^2 X+1 X X^2+X X^2+X 1 0 X+1 X X^2 1 X+1 1 X^2 X^2+X 1 X^2 X+1 1 X+1 0 0 0 0 0 0 0 X 0 X X X^2+X X X^2 0 X X^2+X X^2+X 0 X^2 X^2+X 0 X^2 X X^2+X X^2 0 X 0 0 X 0 X^2 X^2+X X X^2 X^2+X X^2+X X X^2 X X X X^2 0 0 0 X^2 X X X X^2 X^2 X 0 X^2 X^2 X^2 X^2+X X^2+X 0 X^2 0 X^2+X X^2+X X^2+X 0 0 generates a code of length 66 over Z2[X]/(X^3) who´s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+100x^54+260x^55+848x^56+1128x^57+2346x^58+3104x^59+4875x^60+5684x^61+7830x^62+9468x^63+11286x^64+12072x^65+12820x^66+11832x^67+11477x^68+9844x^69+8282x^70+5904x^71+4575x^72+2880x^73+2078x^74+992x^75+762x^76+256x^77+224x^78+56x^79+56x^80+8x^81+16x^82+6x^84+2x^88 The gray image is a linear code over GF(2) with n=264, k=17 and d=108. This code was found by Heurico 1.13 in 205 seconds.