The generator matrix

 1  0  0  0  1  1  1  0  0 X^2 X^2  1  1  1  1  X  1 X^2+X X^2+X  1  1  1  X  0  1  1  X  1  1  X X^2  1  1  1 X^2+X  1  1  0  X  1  X X^2  X X^2  1  1  X  1  1  1  1 X^2  1  1  1  X  1  X  0  1 X^2 X^2  1  1  X  1 X^2  1
 0  1  0  0  0  1  1  1 X^2  1  1  0 X+1 X+1  X  1  0  1  X X^2+X+1 X^2+1  1 X^2  1 X^2+1 X^2+X  0  X X^2+1  1 X^2  X X^2+1 X^2  1 X^2+X+1 X^2+1  X  1  1 X^2+X  1  1 X^2  X X+1  1  X X^2 X^2 X^2  X X^2+X+1  0  X  1 X^2+X  X  1 X^2+X+1  1  1  X X+1  0 X^2 X^2  0
 0  0  1  0  1 X^2 X^2+1  1  1  0  1  X X^2+1 X^2 X^2+1 X^2+1 X^2+1  X  X X^2  0  1  1 X^2 X+1 X+1  1  0 X^2+X+1 X^2+X+1  1 X^2+X X+1 X^2+1  0 X^2+X+1 X^2+X X^2+X X+1 X^2+X+1  1 X^2+X X+1 X^2+X X^2+X X^2  1 X+1 X^2 X^2+X X^2+X+1  1 X+1  1  X X^2+1  1 X^2 X^2+X X^2+1  1 X^2 X+1  0 X^2 X^2+1  1 X^2+X+1
 0  0  0  1 X^2  0 X^2 X^2  1  1 X^2+1 X+1  1 X+1 X+1  0 X^2+X X^2+X+1  1  X X^2+X+1 X+1 X^2  X X^2+X X^2+1 X+1 X^2  1 X^2+1  X X^2+X X^2 X+1  0 X^2+X X+1  1 X+1 X^2+X+1 X^2+1 X^2  X  1 X^2+X+1  1  1  X X+1 X^2 X^2+1 X^2 X^2+1 X^2+1  1  X  1  1 X^2+X X^2+X  1 X+1 X^2+1 X^2  1  X X+1 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+126x^62+332x^63+393x^64+490x^65+442x^66+338x^67+316x^68+274x^69+327x^70+260x^71+187x^72+166x^73+136x^74+90x^75+74x^76+70x^77+41x^78+20x^79+5x^80+8x^81

The gray image is a linear code over GF(2) with n=272, k=12 and d=124.
This code was found by Heurico 1.11 in 0.328 seconds.