The generator matrix 1 0 0 0 0 1 1 1 0 1 X^2 1 1 X 1 1 X^2+X X X^2+X X^2+X X 1 1 1 X 1 1 X^2 1 0 1 1 1 0 X^2 X^2+X 1 1 1 1 1 X^2+X 0 1 X^2+X X^2 X^2+X 1 1 0 X^2+X X^2 X X^2 X 0 1 1 1 0 1 1 0 1 1 0 1 0 0 0 0 X+1 X X^2 X+1 1 0 X^2+1 1 X+1 X^2+X 1 X^2 X 1 1 1 X+1 0 1 X^2 X^2+X 1 X^2+1 X X X+1 1 0 X 1 X^2 X^2 X^2+X 1 X^2 1 X^2 X^2+1 X 0 1 X^2+1 0 1 X^2+X 1 1 X X 1 X X^2+1 X^2+X+1 1 X+1 X^2 X^2 X^2+X+1 X^2 0 0 1 0 0 0 1 X+1 1 X^2+1 X^2 1 X^2+X X^2+1 X^2+1 1 X+1 X 1 X^2+X+1 0 X X^2+X 0 0 1 X^2 1 X+1 1 X+1 X^2+X X X^2 1 X X^2+X+1 X^2+X 0 0 1 0 1 X^2+1 X 1 X^2 X^2+X X X^2+X+1 1 X+1 0 1 0 X 1 X+1 1 X+1 X^2+X 0 1 0 X^2 0 0 0 1 0 1 X^2 X^2+1 1 1 X+1 X X X X^2+X X^2+X+1 X^2+1 1 0 0 0 X+1 X^2+1 X X^2+X+1 X X+1 1 X^2+1 1 X X^2 X^2+1 1 X+1 1 X^2+X 0 X^2+X X^2 X+1 1 X^2+X X^2+X+1 X X^2 X X^2+X X^2+1 1 X^2 X^2+X+1 X^2+X X+1 1 X^2+1 X^2+X+1 1 X^2+X X^2 X^2+1 1 X^2 1 X^2 0 0 0 0 1 1 X^2+1 X X+1 X^2+1 X X+1 X^2+1 X^2+1 0 X^2+1 X^2 1 1 0 1 0 X^2+X+1 1 X^2+1 X^2+X X^2 1 X^2+X 0 X+1 X^2+X X^2+1 X^2+X 0 X^2+1 X^2 1 0 X^2+X+1 X^2+1 X^2+X X^2+X+1 X+1 1 0 X X X X X^2 1 1 X^2+X+1 X+1 X+1 X X^2 X X^2 X^2+1 0 X^2+X+1 X X^2+X 0 0 0 0 0 X 0 X X X X^2+X X^2 X^2 X^2 X^2 X^2+X X X 0 0 0 X^2+X X X^2 X 0 X X^2+X X^2+X X^2+X 0 X^2 X^2+X X^2+X 0 X^2 X^2+X X X^2+X X X^2 X^2 X^2+X 0 X^2+X X^2+X X^2+X X^2+X X^2 0 X 0 X^2+X X X^2 0 X^2 X^2+X X X^2 X^2 X^2+X X X^2+X X generates a code of length 65 over Z2[X]/(X^3) who´s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+217x^54+566x^55+1315x^56+1906x^57+3292x^58+4462x^59+6628x^60+7188x^61+10037x^62+10480x^63+13136x^64+12036x^65+13249x^66+10836x^67+10771x^68+7378x^69+6414x^70+4166x^71+3050x^72+1692x^73+1101x^74+574x^75+347x^76+130x^77+56x^78+20x^79+14x^80+6x^81+2x^82+2x^84 The gray image is a linear code over GF(2) with n=260, k=17 and d=108. This code was found by Heurico 1.13 in 202 seconds.