The generator matrix

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

generates a code of length 34 over Z4 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+111x^24+176x^25+286x^26+456x^27+608x^28+748x^29+986x^30+1218x^31+1258x^32+1402x^33+1505x^34+1580x^35+1492x^36+1314x^37+1049x^38+780x^39+536x^40+338x^41+253x^42+116x^43+87x^44+50x^45+17x^46+10x^47+2x^48+4x^49+1x^52

The gray image is a code over GF(2) with n=68, k=14 and d=24.
This code was found by Heurico 1.10 in 5.45 seconds.