The generator matrix

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

generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+42x^22+26x^23+127x^24+130x^25+283x^26+352x^27+536x^28+718x^29+940x^30+1218x^31+1380x^32+1652x^33+1537x^34+1648x^35+1404x^36+1212x^37+1002x^38+734x^39+525x^40+362x^41+253x^42+112x^43+104x^44+22x^45+32x^46+6x^47+15x^48+7x^50+4x^52

The gray image is a linear code over GF(2) with n=68, k=14 and d=22.
This code was found by Heurico 1.16 in 11.7 seconds.