The generator matrix

1 0 0 0 0 0 0 1 1 1 1 X 1 1 0 1 1 X 1 1 X 0 X 1 1 0 X 1 X 1 0 0 1 0
0 1 0 0 0 0 0 0 0 0 0 0 0 1 X 1 1 0 X+1 0 X X 1 X+1 X 1 1 X+1 1 0 X 1 0 X
0 0 1 0 0 0 0 0 0 0 0 0 0 X 1 1 X+1 X 1 1 0 X X 0 1 1 X+1 X 1 1 1 0 X+1 1
0 0 0 1 0 0 0 1 0 X X+1 1 X 0 X 0 X 0 1 X+1 1 1 1 0 X+1 X X+1 0 1 0 X+1 X X+1 0
0 0 0 0 1 0 0 1 X X+1 X 1 0 0 0 1 1 1 X+1 0 X X+1 0 X 1 0 1 X X+1 X+1 0 X+1 0 0
0 0 0 0 0 1 0 1 X+1 0 X X+1 X 1 1 X+1 0 1 0 X+1 1 X+1 X+1 0 X+1 X+1 X+1 X+1 X+1 0 X+1 X X X
0 0 0 0 0 0 1 X 1 X+1 X+1 X+1 1 X X+1 X+1 X X+1 1 1 1 0 X 0 0 X 1 X+1 0 X X+1 1 X 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+135x^24+608x^26+1238x^28+1944x^30+2642x^32+3048x^34+2908x^36+2072x^38+1113x^40+472x^42+142x^44+48x^46+13x^48

The gray image is a linear code over GF(2) with n=68, k=14 and d=24.
This code was found by Heurico 1.10 in 4.55 seconds.