The generator matrix

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

generates a code of length 35 over Z4 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+117x^28+280x^30+338x^32+284x^34+374x^36+280x^38+210x^40+108x^42+45x^44+8x^46+3x^48

The gray image is a code over GF(2) with n=70, k=11 and d=28.
This code was found by Heurico 1.16 in 0.265 seconds.