The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  X  1  1  1  X  X  1  1  1  1  1  X  X  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  X  X  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  X  0  X  X  0  X  0  0  0  X  0  X  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  X  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  0  0  X  X  X  0  X  0  X  X  X  X  X  X  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  0  X  0  0  X  X  X  X  0  0  0  X  0  X  X  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  X  0  X  0  X  X  X  X  X  0  0  0  0  0  X  X  X  0  0  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  X  X  0  0  X  X  X  X  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  X  0  X  X  X  0  0  0  X  X  0  0  X  0  X  X  X  X  0  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  0  X  X  X  X  X  0  0  0  X  0  0  X  X  X  X  0  0  0  X  X
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  0  X  X  0  0  0  X  X  X  0  0  0  X  X  0  X  X
 0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  X  0  X  0  X  0  X  0  0  X  X  0  0  X  0  X  0

generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+63x^20+71x^22+203x^24+161x^26+64x^27+330x^28+192x^29+347x^30+576x^31+524x^32+1216x^33+652x^34+1216x^35+568x^36+576x^37+417x^38+192x^39+217x^40+64x^41+254x^42+126x^44+121x^46+15x^48+20x^50+1x^52+4x^54+1x^58

The gray image is a linear code over GF(2) with n=68, k=13 and d=20.
This code was found by Heurico 1.16 in 7.5 seconds.