The generator matrix

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

generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+98x^62+156x^63+179x^64+172x^65+177x^66+184x^67+174x^68+184x^69+154x^70+172x^71+135x^72+156x^73+66x^74+16x^76+6x^78+4x^80+5x^82+6x^86+1x^88+2x^92

The gray image is a linear code over GF(2) with n=272, k=11 and d=124.
This code was found by Heurico 1.16 in 0.407 seconds.