The generator matrix

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

generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+142x^63+183x^64+294x^65+225x^66+246x^67+188x^68+188x^69+127x^70+112x^71+88x^72+66x^73+48x^74+30x^75+16x^76+32x^77+12x^78+30x^79+4x^80+12x^81+3x^82+1x^86

The gray image is a linear code over GF(2) with n=272, k=11 and d=126.
This code was found by Heurico 1.16 in 0.309 seconds.