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

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+48x^62+254x^64+320x^66+256x^68+32x^70+64x^74+48x^78+1x^128

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 0.266 seconds.