The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  0  1  1  0  1  1  0  1  2  1  1  1  1  2  1  1
 0  1  1  0  1  1  0  1  1  0  1  1  0  3  1  0  3  1  1  3  1  1  0  0  1  3  1  0  2  0  2  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  2  2  2  2  2  2  0  0  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  2  0  2  0  0  2  2  2  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  2  0  2  2  0  2  2  0  2  2  0  2  2  0  0  2  2  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  0  0  2  2  0  0  2  2  2  0  0  0  2  0  2  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  2  0  2  2  0  2  0  0  2  2  0  2  2  0  0  0  2  2  2  0
 0  0  0  0  0  0  0  2  0  0  0  2  2  2  0  0  2  2  0  0  2  2  2  2  2  2  0  0  0  2  2  2  0  0
 0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  0  2  0  2  0  0  2  2  2  0  0  2  0  0  0  0  0  2  0
 0  0  0  0  0  0  0  0  0  2  0  2  0  0  2  2  0  0  2  0  0  2  2  2  2  2  0  2  0  0  0  2  0  2
 0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  2  0  0  0  2  0  2  0  2  0  0  2  2  0  2  0  2  2  0

generates a code of length 34 over Z4 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+46x^22+14x^23+102x^24+50x^25+178x^26+150x^27+205x^28+370x^29+513x^30+620x^31+576x^32+820x^33+778x^34+876x^35+735x^36+644x^37+365x^38+326x^39+353x^40+154x^41+126x^42+62x^43+51x^44+10x^45+35x^46+23x^48+6x^50+1x^52+1x^54+1x^56

The gray image is a code over GF(2) with n=68, k=13 and d=22.
This code was found by Heurico 1.16 in 3.54 seconds.