The generator matrix
1 0 1 1 1 0 1 1 0 1 1 0 0 X 1 1 1 1 1 1 1 1 0 1 1 0 1 X 0 1 X X 1 1
0 1 1 0 1 1 0 1 1 X X+1 1 1 1 0 0 0 X X+1 X+1 X+1 1 1 0 0 1 X+1 0 1 1 1 0 0 0
0 0 X 0 0 0 0 0 0 0 X 0 X X 0 X X 0 0 0 X X 0 0 X X 0 0 X X 0 0 0 0
0 0 0 X 0 0 0 0 0 X 0 0 X X 0 X 0 X 0 X X 0 0 0 X 0 0 X 0 X 0 X 0 0
0 0 0 0 X 0 0 0 0 0 X X 0 X X 0 X 0 0 X 0 X 0 X 0 X X X X X X X 0 0
0 0 0 0 0 X 0 0 0 0 0 X X X 0 0 0 0 X X X X 0 X 0 0 0 X X X 0 0 0 0
0 0 0 0 0 0 X 0 0 X 0 X X 0 X 0 0 X X 0 X 0 X 0 X 0 0 0 0 0 X X 0 0
0 0 0 0 0 0 0 X 0 0 X X X 0 X X 0 0 X 0 0 X 0 0 0 0 X X X 0 X 0 0 0
0 0 0 0 0 0 0 0 X 0 0 0 0 0 X X X X X X X X 0 X 0 0 0 0 X X 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+60x^24+36x^26+208x^28+196x^30+375x^32+300x^34+369x^36+204x^38+201x^40+32x^42+62x^44+2x^48+1x^52+1x^56
The gray image is a linear code over GF(2) with n=68, k=11 and d=24.
This code was found by Heurico 1.16 in 0.248 seconds.