The generator matrix

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

generates a code of length 65 over Z2[X]/(X^3) who�s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+98x^58+205x^60+32x^61+218x^62+144x^63+292x^64+176x^65+306x^66+112x^67+146x^68+48x^69+102x^70+92x^72+38x^74+29x^76+4x^78+2x^80+2x^82+1x^112

The gray image is a linear code over GF(2) with n=260, k=11 and d=116.
This code was found by Heurico 1.16 in 0.403 seconds.