The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+47x^22+102x^23+261x^24+384x^25+625x^26+774x^27+1180x^28+1486x^29+1775x^30+2470x^31+2624x^32+2962x^33+3018x^34+2968x^35+2905x^36+2448x^37+2026x^38+1566x^39+1167x^40+824x^41+517x^42+290x^43+162x^44+82x^45+55x^46+22x^47+19x^48+6x^49+1x^52+1x^54

The gray image is a code over GF(2) with n=68, k=15 and d=22.
This code was found by Heurico 1.10 in 19 seconds.