The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+58x^22+12x^23+156x^24+110x^25+308x^26+344x^27+592x^28+702x^29+926x^30+1224x^31+1275x^32+1692x^33+1504x^34+1696x^35+1354x^36+1260x^37+950x^38+716x^39+568x^40+310x^41+292x^42+104x^43+132x^44+22x^45+50x^46+16x^48+8x^50+2x^52

The gray image is a code over GF(2) with n=68, k=14 and d=22.
This code was found by Heurico 1.16 in 11.6 seconds.