The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  X  1  1  1  0  1  1  1  0  0  0  1  1  1  1  0  1  X  1  1  1  1  1
 0  1  1  0  1  1  0  1  1  0 X+1  1  0 X+1  0  1 X+1 X+1 X+1  1  1  1  0 X+1  X  X  1  1  1  0 X+1 X+1  0  0
 0  0  X  0  0  0  0  0  0  0  X  0  0  0  X  X  0  0  X  0  X  0  X  0  X  0  X  X  X  0  X  X  X  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  0  0  X  X  X  X  X  0  0  0  X
 0  0  0  0  X  0  0  0  0  0  X  0  X  0  X  0  X  0  X  X  X  0  0  0  0  X  X  0  0  X  X  X  0  X
 0  0  0  0  0  X  0  0  0  0  0  X  X  0  X  0  0  X  X  0  X  0  X  X  0  0  0  0  X  X  0  0  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  X  0  X  0  X  X
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  X  0  X  X  X  0  0  X  X  X  X  0  0  X  0  0  0  X  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  0  X  X  X  0  0  0  X  X  0  X  X  X  0  X  X  0  X  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  0  X  0  0  X  X  X  X  X  X  X  X  0  0  0  X  X  0  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+41x^24+130x^26+277x^28+504x^30+715x^32+780x^34+701x^36+504x^38+261x^40+130x^42+44x^44+6x^48+1x^52+1x^60

The gray image is a linear code over GF(2) with n=68, k=12 and d=24.
This code was found by Heurico 1.16 in 1.06 seconds.