The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  2  1  1  1  1  1  1  2  2  2  1  1  2  1  2
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  2  2  2  2  2  2  2  2
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  2  0  2  2  0  2  0  0  0  0  2  2  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  0  2  2  2  0  0  2  0  2
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  0  0  2  2  2  0  0  2  0  2  2  2  2  2  0  0  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  0  2  0  0  2  2  0  0  2  0  0  2  2  0  2  0  2
 0  0  0  0  0  0  0  2  0  0  0  0  0  2  2  0  2  0  2  2  2  2  2  2  2  2  0  0  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  2  0  0  0  0  2  0  0  0  0  0  0  2  2  2  0  0  0  2  2  2  0  0  2  2  0
 0  0  0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  2  0  0  0  2  2  2  2  0  2  0  2  2  2  2  0  0
 0  0  0  0  0  0  0  0  0  0  2  0  0  2  0  2  2  2  2  2  0  0  0  0  2  2  2  2  0  2  2  2  0  0
 0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  2  0  2  2  0  0  2  0  0  2  0  0  2  0  0  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  2  2  0  2  0  2  0  2  0  0  2  2  2  2  0  2  0

generates a code of length 34 over Z4 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 code over GF(2) with n=68, k=14 and d=20.
This code was found by Heurico 1.16 in 17.1 seconds.