The generator matrix

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

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+134x^62+308x^63+399x^64+466x^65+451x^66+378x^67+298x^68+370x^69+252x^70+192x^71+271x^72+132x^73+123x^74+110x^75+80x^76+50x^77+32x^78+32x^79+7x^80+6x^81+4x^83

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 0.727 seconds.