The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+53x^22+68x^23+232x^24+342x^25+511x^26+812x^27+1037x^28+1442x^29+1839x^30+2328x^31+2891x^32+3132x^33+3345x^34+3192x^35+2679x^36+2468x^37+1947x^38+1492x^39+1148x^40+718x^41+425x^42+284x^43+187x^44+90x^45+65x^46+16x^47+16x^48+7x^50+1x^52

The gray image is a code over GF(2) with n=68, k=15 and d=22.
This code was found by Heurico 1.16 in 40.6 seconds.