The generator matrix

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

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+84x^61+202x^62+256x^63+308x^64+368x^65+391x^66+366x^67+316x^68+324x^69+366x^70+332x^71+264x^72+206x^73+141x^74+66x^75+24x^76+16x^77+10x^78+16x^79+8x^80+8x^81+10x^82+4x^83+4x^84+1x^88+2x^89+2x^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 1.09 seconds.