The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+42x^22+102x^23+228x^24+388x^25+617x^26+804x^27+1126x^28+1474x^29+1935x^30+2346x^31+2676x^32+3002x^33+3022x^34+3088x^35+2865x^36+2460x^37+1928x^38+1522x^39+1082x^40+768x^41+581x^42+300x^43+200x^44+98x^45+63x^46+30x^47+13x^48+2x^49+4x^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 42.3 seconds.