The generator matrix

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

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+111x^24+210x^26+670x^28+848x^30+1512x^32+1468x^34+1552x^36+856x^38+653x^40+194x^42+94x^44+8x^46+11x^48+4x^52

The gray image is a linear code over GF(2) with n=68, k=13 and d=24.
This code was found by Heurico 1.16 in 3.64 seconds.