The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+152x^22+158x^23+542x^24+614x^25+1316x^26+1478x^27+2299x^28+2868x^29+3973x^30+4930x^31+5134x^32+6112x^33+5761x^34+6652x^35+5398x^36+4776x^37+3874x^38+3138x^39+2488x^40+1350x^41+1134x^42+494x^43+495x^44+148x^45+161x^46+46x^47+27x^48+4x^49+13x^50

The gray image is a code over GF(2) with n=68, k=16 and d=22.
This code was found by Heurico 1.10 in 80.5 seconds.