The generator matrix

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

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+150x^22+144x^23+544x^24+614x^25+1334x^26+1554x^27+2310x^28+2812x^29+3827x^30+4814x^31+5268x^32+6364x^33+5833x^34+6376x^35+5284x^36+5028x^37+3960x^38+2960x^39+2334x^40+1402x^41+1244x^42+502x^43+478x^44+160x^45+159x^46+34x^47+37x^48+4x^49+5x^50

The gray image is a linear code over GF(2) with n=68, k=16 and d=22.
This code was found by Heurico 1.11 in 76.9 seconds.