The generator matrix

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

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+30x^26+50x^27+125x^28+114x^29+101x^30+178x^31+201x^32+170x^33+120x^34+174x^35+196x^36+182x^37+112x^38+102x^39+98x^40+46x^41+17x^42+8x^43+15x^44+3x^46+4x^48+1x^58

The gray image is a linear code over GF(2) with n=68, k=11 and d=26.
This code was found by Heurico 1.16 in 0.237 seconds.