The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  1  0  1  1  1  1  0  1  1  1  1  0  X  1  1  1  1  1  1  1
 0  1  1  0  1  1  0  1  1  0  1  1  0  X X+1  1  0 X+1 X+1  0  1 X+1 X+1 X+1  X  1  1  0 X+1 X+1  0  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  X  X  0  0  X  X  X  X  0  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  X  X  X  0  0  0  X  X  0  X  X  0  X  X  X  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  X  0  X  0  X  X  X  0  X  X  X  0  X  X  0  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  0  X  0  X  0  X  X  X  X  X  0  0  0  X  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  X  X  X  X  0  X  0  X  X  X  X  X  0  0  0  X  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  0  X  X  0  X  0  0  0  X  X  X  X  0  X  X  0
 0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  X  X  X  X  X  X  0  X  X  0  0  X  0  0  0  X  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  X  0  X  X  X  0  0  0  X  X  0  0  0  0  X  0  0  X  0  0
 0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  0  X  X  0  0  X  0  0  0  0  X  0  X  0

generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+35x^20+106x^22+226x^24+435x^26+964x^28+1757x^30+2839x^32+3579x^34+2902x^36+1817x^38+998x^40+385x^42+188x^44+95x^46+32x^48+17x^50+7x^52+1x^54

The gray image is a linear code over GF(2) with n=68, k=14 and d=20.
This code was found by Heurico 1.16 in 11.1 seconds.