The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  X  0  X  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1  1
 0  1  0  0  0  1  1  1  0  0  1 X+1  1  0  1  1  X  1  0  0  X  0  1 X+1 X+1  1  1  X  X  0  1  0  1  0
 0  0  1  0  1  1  0  1  0  1  1  0  0  1  1  X  1  1  1  X  1  0  0 X+1 X+1  0  0  1  1  1 X+1  X X+1  0
 0  0  0  1  1  0  1  1  1  0  1  0  1  1  0  X  X  0 X+1 X+1  X  X  1  1  0  X  1  0  1 X+1  0 X+1  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  0  0  X  X  0  X  0  X  X  X  0  X  0  0  X  0  0  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  0  X  0  X  X  0  0  X  0  0  X  0  0  X  X  X  0  X  0
 0  0  0  0  0  0  X  0  0  0  0  X  0  0  X  X  0  X  0  0  X  0  0  X  0  0  X  X  0  0  X  X  0  0
 0  0  0  0  0  0  0  X  0  0  0  X  0  0  X  X  0  X  X  X  0  X  X  0  0  0  0  0  0  X  0  0  X  X
 0  0  0  0  0  0  0  0  X  0  0  0  X  0  0  0  0  0  0  X  X  X  X  0  X  X  X  0  0  0  X  X  0  X
 0  0  0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  X  X  0  0  X  0  X  0  X  X  0  X  X  0  0  0  X
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  0  0  X  X  0  X  0  X  X  0  0  X  0  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+54x^22+74x^23+216x^24+284x^25+567x^26+794x^27+1109x^28+1410x^29+1878x^30+2464x^31+2747x^32+3138x^33+3151x^34+3156x^35+2827x^36+2516x^37+1978x^38+1450x^39+1084x^40+768x^41+501x^42+242x^43+187x^44+74x^45+58x^46+12x^47+16x^48+2x^49+5x^50+5x^52

The gray image is a linear code over GF(2) with n=68, k=15 and d=22.
This code was found by Heurico 1.16 in 39.7 seconds.