The generator matrix
1 0 0 0 1 1 1 0 1 X 1 0 1 X 1 1 1 1 1 1 0 X 1 0 0 X 1 1 0 1 0 0 1 1
0 1 0 0 0 1 1 1 X+1 X 0 1 X 1 X X X+1 X+1 X X 1 X X 1 1 1 X+1 X 1 X X 1 X X+1
0 0 1 0 1 1 0 1 1 1 X 0 X+1 1 X+1 X 0 0 X 0 0 1 X X+1 1 X+1 0 0 X 1 1 1 X X+1
0 0 0 1 1 0 1 X+1 1 X+1 X+1 X+1 X 0 0 X X+1 X X+1 0 X+1 X+1 0 X+1 X X 1 X+1 X X+1 X+1 1 X 0
0 0 0 0 X 0 0 X 0 0 X X X X X 0 0 X 0 0 0 X 0 X 0 0 X X 0 0 X 0 X X
0 0 0 0 0 X 0 0 0 0 0 0 X X X 0 X 0 0 X X 0 X X 0 X X 0 X X X 0 0 0
0 0 0 0 0 0 X 0 0 X X X X X 0 X 0 0 0 X X X 0 0 X X 0 0 0 X X 0 0 0
generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 27.
Homogenous weight enumerator: w(x)=1x^0+54x^27+161x^28+136x^29+67x^30+170x^31+246x^32+166x^33+91x^34+158x^35+248x^36+158x^37+68x^38+110x^39+96x^40+50x^41+28x^42+20x^43+15x^44+2x^45+1x^46+1x^48+1x^50
The gray image is a linear code over GF(2) with n=68, k=11 and d=27.
This code was found by Heurico 1.16 in 1.58 seconds.