The generator matrix

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

generates a code of length 65 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+29x^52+121x^54+36x^55+235x^56+112x^57+462x^58+320x^59+900x^60+740x^61+1549x^62+1176x^63+1865x^64+1392x^65+1904x^66+1168x^67+1451x^68+696x^69+826x^70+356x^71+529x^72+128x^73+198x^74+16x^75+78x^76+4x^77+42x^78+24x^80+12x^82+6x^84+5x^86+2x^88+1x^94

The gray image is a linear code over GF(2) with n=260, k=14 and d=104.
This code was found by Heurico 1.16 in 15 seconds.