The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+36x^24+64x^25+155x^26+250x^27+346x^28+366x^29+520x^30+530x^31+576x^32+792x^33+751x^34+828x^35+733x^36+660x^37+500x^38+364x^39+294x^40+152x^41+101x^42+74x^43+56x^44+14x^45+20x^46+2x^47+5x^48+1x^50+1x^52

The gray image is a code over GF(2) with n=68, k=13 and d=24.
This code was found by Heurico 1.16 in 3.49 seconds.