The generator matrix

 1  0  0  1  1  1 X^2+X  1  X  1  1  1  0  X  0  X  0  1  1  1  1  1  1  1  1 X^2+X X^2 X^2+X X^2  1  1 X^2+X  1  1  0 X^2  0  1  1  1  1  1 X^2+X  1 X^2+X  1  1  0  X  1  1  1  1  1  1 X^2+X  0  0  1 X^2  1  X  1 X^2+X  1
 0  1  0  0  1 X+1  1 X^2+X  0 X+1 X^2+X  1  1  1 X^2+X  1  1 X^2+1 X+1 X^2+X+1  0 X^2+X X^2+X X^2+X+1  X  1  X  0  1 X^2 X^2+X+1  1 X^2+1 X^2+1  1  1  X  0 X^2+X X^2+X+1 X^2+X  X  1  X  1 X^2 X^2+1  1  1  1  X X^2+X+1 X^2  0 X^2+1 X^2+X  X  0  1  1 X^2+1  1 X^2  1  0
 0  0  1  1  1  0  1  1  1 X^2+1  0 X^2  1 X^2  1 X+1 X^2+X  X X+1  0  1  X X^2+X X^2+1 X^2+X+1 X^2+1  1  1  0 X^2+X+1  0 X^2+1 X^2+X+1  X  X  1  1  X  0 X+1  1 X+1 X+1  0 X^2 X^2+1 X^2+X+1  1 X^2 X^2+X X^2+X+1 X^2+X+1 X^2+X X+1 X^2+X  1  1  1 X^2+X  0 X^2+1 X+1 X^2  0 X^2+1
 0  0  0  X  0  0 X^2 X^2 X^2 X^2+X  X  X X^2+X  X  X  0  0 X^2  0 X^2+X X^2 X^2 X^2+X X^2+X  X  X  X  0 X^2+X X^2+X  0 X^2+X  0 X^2  0 X^2 X^2+X X^2+X  X  X  X  0  X X^2  0  X X^2+X  0 X^2+X X^2+X X^2 X^2+X  0 X^2  X  0 X^2 X^2 X^2 X^2+X  0  0  X X^2+X  X
 0  0  0  0  X X^2  X X^2+X X^2+X X^2  X X^2+X  0  X  0  X X^2  0  X X^2+X  X X^2 X^2+X  0  0  0 X^2+X  0 X^2 X^2+X  X X^2+X  0 X^2+X  X X^2  X X^2 X^2 X^2+X X^2+X  0 X^2+X X^2+X  0  X X^2 X^2+X X^2+X X^2  0  X  X  X X^2+X X^2 X^2+X X^2  X  0 X^2 X^2+X  0 X^2 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+292x^58+180x^59+755x^60+356x^61+1070x^62+372x^63+1094x^64+316x^65+1056x^66+316x^67+844x^68+300x^69+592x^70+140x^71+272x^72+52x^73+100x^74+16x^75+33x^76+26x^78+9x^80

The gray image is a linear code over GF(2) with n=260, k=13 and d=116.
This code was found by Heurico 1.16 in 15.6 seconds.