The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  X  1  1  1  1  1  1  X  X  X  1  1  X  1  X
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X
 0  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  X  X  X  X  X  X  X  X
 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  0  X  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  X  X  0  X  X  X  0  0  X  0  X
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  0  0  X  X  X  0  0  X  0  X  X  X  X  X  0  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  0  X  0  0  X  X  0  0  X  0  0  X  X  0  X  0  X
 0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  0  X  0  X  X  X  X  X  X  X  X  0  0  X  X  X  X  X  X
 0  0  0  0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  0  0  X  X  X  0  0  0  X  X  X  0  0  X  X  0
 0  0  0  0  0  0  0  0  0  X  0  0  0  X  0  X  X  X  0  0  0  X  X  X  X  0  X  0  X  X  X  X  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  0  X  X  X  X  0  X  X  X  0  0
 0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  0  X  X  0  0  X  0  0  X  0  0  X  0  0  X  X
 0  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  X  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+126x^20+649x^24+32x^26+1352x^28+896x^30+4053x^32+2240x^34+3876x^36+896x^38+1558x^40+32x^42+520x^44+138x^48+14x^52+1x^56

The gray image is a linear code over GF(2) with n=68, k=14 and d=20.
This code was found by Heurico 1.16 in 18.7 seconds.