The generator matrix

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

generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+60x^58+108x^59+163x^60+316x^61+424x^62+592x^63+712x^64+772x^65+733x^66+646x^67+753x^68+694x^69+628x^70+520x^71+352x^72+288x^73+166x^74+96x^75+48x^76+42x^77+23x^78+18x^79+14x^80+13x^82+2x^83+4x^84+2x^87+1x^88+1x^94

The gray image is a linear code over GF(2) with n=268, k=13 and d=116.
This code was found by Heurico 1.16 in 4.57 seconds.