The generator matrix

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

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+184x^62+220x^63+482x^64+344x^65+546x^66+284x^67+445x^68+240x^69+312x^70+220x^71+269x^72+108x^73+154x^74+68x^75+93x^76+40x^77+46x^78+8x^79+20x^80+4x^81+4x^82+2x^84+2x^86

The gray image is a linear code over GF(2) with n=272, k=12 and d=124.
This code was found by Heurico 1.16 in 0.94 seconds.