The generator matrix

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

generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+56x^26+138x^27+194x^28+262x^29+295x^30+324x^31+313x^32+324x^33+323x^34+310x^35+308x^36+312x^37+329x^38+210x^39+170x^40+124x^41+52x^42+40x^43+6x^44+2x^45+2x^47+1x^58

The gray image is a linear code over GF(2) with n=68, k=12 and d=26.
This code was found by Heurico 1.10 in 0.343 seconds.