The generator matrix

 1  0  0  1  1  1  0  1 X^2  1  1  X X^2+X  1  1  X  0  1  1  1  1  0  1  1 X^2+X X^2+X X^2+X  1  0  0 X^2+X  X X^2+X  1 X^2  1  1  0 X^2  1  1 X^2 X^2+X  1 X^2  1  1 X^2+X  X X^2+X  1 X^2  1  1  1  X  1  X  0  1 X^2+X  1 X^2  0  1  X  1  1
 0  1  0  0  1 X^2+1  1  X  1  1 X^2+X  1 X^2 X^2+X+1  0  1 X^2+X X^2+X+1  X X^2+X+1 X^2+X  1 X+1 X^2  1  1 X^2+X X^2+1  1  1  1  1  1  0  0 X^2+X X^2  1  1  X X^2+X+1  1 X^2+X X^2+X  1  1 X^2+1  1 X^2  1  X  1 X^2+1 X^2+X+1  1  1 X^2+X+1  1  1  1 X^2+X X+1  1 X^2+X X^2+X+1  1 X^2  0
 0  0  1 X+1 X^2+X+1  0 X+1 X^2+1 X^2+X  1 X^2 X^2+1  1 X^2  1 X^2+X  1 X^2+X  X  1 X^2+X+1 X^2+X+1 X+1 X^2+X X^2 X+1  1  X  1  X X^2+X  1 X+1  1  1 X+1  X X^2 X^2+X+1 X+1 X^2+1 X^2+X+1  1 X+1  1 X^2+X+1  1  X  1 X^2+1  0 X^2+1  0 X^2+X+1 X^2+X+1 X^2 X^2+X X^2+1  0  1  1 X^2+X X^2+X  1  0  0  0 X^2
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2
 0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2  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+136x^63+239x^64+236x^65+299x^66+212x^67+130x^68+166x^69+136x^70+110x^71+89x^72+82x^73+58x^74+44x^75+48x^76+22x^77+17x^78+10x^79+5x^80+6x^81+1x^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 0.332 seconds.