The generator matrix

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

generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+146x^62+134x^64+270x^66+208x^68+154x^70+39x^72+58x^74+12x^78+1x^80+1x^120

The gray image is a linear code over GF(2) with n=268, k=10 and d=124.
This code was found by Heurico 1.16 in 61.1 seconds.