The generator matrix

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

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+114x^64+390x^65+122x^66+410x^67+99x^68+234x^69+72x^70+148x^71+54x^72+92x^73+26x^74+42x^75+8x^76+26x^77+4x^78+26x^79+11x^80+26x^81+1x^84

The gray image is a linear code over GF(2) with n=272, k=11 and d=126.
This code was found by Heurico 1.11 in 0.188 seconds.