The generator matrix

 1  0  0  1  1  1 X^2+X  1  X  0 X^2  1  1  1  1  1  X  1  X  0  1  0  1  1 X^2  X  1  1  0  1  0  1  1  1  X  0 X^2  1  1  1  1 X^2+X  1  1  X X^2  1  1  1  1  X  0  1  X  X X^2+X X^2+X  1  0  1 X^2  1  1  1 X^2
 0  1  0  0  1  1  1 X^2  1  0  1 X^2 X+1 X+1 X^2+1 X^2+1 X^2+X X^2+X  1 X^2+X  1  1  X X^2  1  1 X^2+X+1  X  1 X^2+X  1 X+1 X+1  1  1 X^2+X  1 X^2+X+1  0 X^2+X X^2+X X^2+X X^2+X+1 X^2+X  1  1 X^2  0 X+1 X^2+X+1  0  1 X+1  1  X  1 X^2+X  1  1  0 X^2  0 X+1  0  0
 0  0  1  1  1  0  1 X^2 X^2+1  1 X^2+X X^2+X+1  0 X+1 X^2+1  X  1  0  1  1  X  0 X+1 X^2+X X^2+1 X^2+X  1 X^2+1 X^2 X^2+1 X+1 X^2+1  X X^2  X  1  X X^2+X  1 X^2 X^2  1 X^2+1 X^2+X+1  0 X+1  1  X X^2+X+1  0  1 X^2+X+1 X^2+1 X^2  1 X^2+X+1  1  X X^2+1  X  1  0  0 X^2+1  0
 0  0  0  X  0  0  0  0  0  0  0  X X^2  0 X^2  X X^2+X  X X^2+X  X X^2+X X^2  X  X X^2+X  X  X  0 X^2+X  0 X^2  X X^2  X X^2+X  X  0 X^2+X  0 X^2 X^2+X X^2+X  X X^2+X  X  0  0 X^2  X X^2 X^2+X  X  0 X^2  0 X^2 X^2  0 X^2  X X^2+X X^2+X  0 X^2+X X^2
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0 X^2+X X^2+X X^2 X^2 X^2  X  X  X X^2  X X^2 X^2+X  X X^2+X  X X^2+X  X X^2  X X^2+X X^2 X^2  X X^2  X X^2+X X^2+X  0 X^2  0 X^2+X X^2 X^2 X^2 X^2+X X^2+X  X  X  X X^2+X X^2  X X^2  X
 0  0  0  0  0  X X^2+X X^2+X X^2  X  X  X  0 X^2+X  0 X^2  X X^2+X X^2+X  0  X  X X^2+X  0  0 X^2 X^2  X  X X^2+X  X  X  X X^2+X X^2  0 X^2 X^2 X^2 X^2+X X^2 X^2  0  0  0  X  0 X^2  0 X^2 X^2 X^2+X  0 X^2+X X^2+X  0 X^2  X  0 X^2+X X^2  0  0 X^2+X X^2+X

generates a code of length 65 over Z2[X]/(X^3) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+128x^55+277x^56+560x^57+806x^58+1200x^59+1697x^60+1886x^61+2430x^62+2828x^63+3018x^64+3090x^65+3023x^66+2950x^67+2493x^68+2046x^69+1581x^70+1064x^71+660x^72+426x^73+261x^74+128x^75+100x^76+52x^77+25x^78+20x^79+8x^80+4x^81+2x^82+2x^83+2x^84

The gray image is a linear code over GF(2) with n=260, k=15 and d=110.
This code was found by Heurico 1.16 in 45.8 seconds.