The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+111x^24+210x^26+670x^28+848x^30+1512x^32+1468x^34+1552x^36+856x^38+653x^40+194x^42+94x^44+8x^46+11x^48+4x^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 3.68 seconds.