The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+133x^24+140x^25+299x^26+438x^27+579x^28+770x^29+1032x^30+1156x^31+1266x^32+1544x^33+1444x^34+1564x^35+1482x^36+1300x^37+1006x^38+808x^39+555x^40+316x^41+263x^42+126x^43+75x^44+26x^45+48x^46+4x^47+5x^48+2x^50+2x^54

The gray image is a code over GF(2) with n=68, k=14 and d=24.
This code was found by Heurico 1.16 in 25 seconds.