The generator matrix

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

generates a code of length 34 over Z4 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+71x^28+197x^30+224x^32+144x^34+145x^36+100x^38+87x^40+36x^42+16x^44+3x^46

The gray image is a code over GF(2) with n=68, k=10 and d=28.
This code was found by Heurico 1.16 in 0.0615 seconds.