The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+95x^28+167x^30+193x^32+186x^34+140x^36+120x^38+62x^40+38x^42+21x^44+1x^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 0.0682 seconds.