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.