The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  X  1  1  1  X  1  0  X  0  1  0  1  X  X  1  X  0  1  X
 0  1  0  0  0  1  1  1  0  0 X+1 X+1  1  1  0  0  0 X+1  1  X  1  1  1  1  X  1  X  0  1  X  0  1  0  1
 0  0  1  0  1  1  0  1  0  1  1  X  0  1  1  1  X  1 X+1  1  0  0  0  1  1 X+1  0  X  1 X+1  1  0  0  0
 0  0  0  1  1  0  1  1  1  0  1  0  1  0 X+1  1  X  1  0  X  1  0  1  X X+1  1  1  1  0  0  X  0  1  1
 0  0  0  0  X  0  0  0  0  0  0  0  X  0  X  X  0  0  0  0  X  0  X  0  X  0  X  0  X  X  0  X  X  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  0  X  X  X  X  0  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  0  0  0  0  X  X  0  X  X  0  0  X  X  X  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  X  X  X  X  X  0  X  X  0  X  0  X  X  X  X  X  X  X  X  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  X  0  X  X  X  X  0  0  0  X  X  X  X  0  X  X  0  X  X
 0  0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  0  X  0  X  0  0  0  0  0  X  X  X  0  X  X  0  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+207x^24+520x^26+1252x^28+1754x^30+2895x^32+2976x^34+3026x^36+1972x^38+1120x^40+424x^42+184x^44+34x^46+16x^48+2x^52+1x^56

The gray image is a linear code over GF(2) with n=68, k=14 and d=24.
This code was found by Heurico 1.16 in 33.2 seconds.