The generator matrix

 1  0  0  1  1  1  0  1  1 X^2  1  X  1  0  1 X^2+X  1 X^2+X  1  1  1  1 X^2  1  1  X  X X^2+X X^2+X X^2  1  1  X  1  1  1  1  1  1  1  1 X^2+X X^2  1  1  1  X X^2+X  0  1  1  1  1  1  1 X^2  0  X  0 X^2+X  1 X^2+X X^2 X^2+X X^2+X X^2 X^2+X X^2+X
 0  1  0  0  1  1  1 X^2  1  1 X^2+1  1 X^2+X X^2+X X+1  1  X  X X^2+X+1 X^2+X  X X+1  1  0 X^2+X+1 X^2  1  1  1  1 X^2  X  1 X^2+X+1 X+1 X^2+X+1 X^2 X+1  X  1 X^2+1  1  1  0  0  1  1  0  1  X X^2 X+1 X^2+X X^2+X+1  0  1  X  1  1  1  1  1  1  1  1  X  1  0
 0  0  1 X+1 X^2+X+1  0 X+1  X  1 X^2+1  X X^2+X X+1  1  X  0  X  1 X^2+X+1 X^2+1 X^2 X^2+1  X X^2+1  0  1  1 X^2+1 X^2+1 X^2 X^2  1 X+1 X^2+1  X X^2 X^2+X X+1  X  0 X^2+X+1 X+1 X+1 X^2+X+1 X+1  1  X  1 X^2+1 X+1 X^2+1  1 X^2+X+1  X X+1  X  1 X^2+1 X+1 X^2+X+1 X^2  1 X^2+1 X^2+X+1 X^2+X X^2 X^2+X  1
 0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0 X^2  0
 0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 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+305x^62+802x^64+818x^66+695x^68+513x^70+402x^72+338x^74+126x^76+61x^78+19x^80+12x^82+3x^84+1x^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 3.22 seconds.