The generator matrix

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

generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+60x^24+36x^26+208x^28+196x^30+375x^32+300x^34+369x^36+204x^38+201x^40+32x^42+62x^44+2x^48+1x^52+1x^56

The gray image is a linear code over GF(2) with n=68, k=11 and d=24.
This code was found by Heurico 1.16 in 0.248 seconds.