The generator matrix

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

generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+110x^61+150x^62+266x^63+332x^64+362x^65+408x^66+326x^67+356x^68+340x^69+376x^70+286x^71+234x^72+236x^73+134x^74+66x^75+23x^76+18x^77+16x^78+8x^79+7x^80+18x^81+2x^82+8x^83+4x^84+4x^85+2x^86+2x^88+1x^92

The gray image is a linear code over GF(2) with n=272, k=12 and d=122.
This code was found by Heurico 1.16 in 1.08 seconds.