The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+193x^24+510x^26+1307x^28+1812x^30+2768x^32+2958x^34+3053x^36+2000x^38+1175x^40+370x^42+181x^44+28x^46+23x^48+2x^50+3x^52

The gray image is a code over GF(2) with n=68, k=14 and d=24.
This code was found by Heurico 1.16 in 40.3 seconds.