The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+68x^28+84x^30+223x^32+132x^34+182x^36+156x^38+136x^40+12x^42+20x^44+8x^48+2x^52

The gray image is a code over GF(2) with n=70, k=10 and d=28.
This code was found by Heurico 1.16 in 0.0771 seconds.