The generator matrix

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

generates a code of length 65 over Z2[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+252x^57+394x^58+768x^59+930x^60+1244x^61+1184x^62+1348x^63+1376x^64+1570x^65+1457x^66+1414x^67+1143x^68+1104x^69+691x^70+618x^71+311x^72+294x^73+141x^74+68x^75+39x^76+16x^77+5x^78+6x^79+8x^80+2x^83

The gray image is a linear code over GF(2) with n=260, k=14 and d=114.
This code was found by Heurico 1.13 in 3.84 seconds.