The generator matrix

 1  0  0  0  0  1  1  1  2  0  1  1  2  1  0  1  1  2  2  1  2  0  1  2  0  1  1  0  2  2  1  0  0  2  2
 0  1  0  0  0  0  0  0  0  0  0  2  1  2  1  3  2  1  1  3  1  0  2  1  1  3  1  2  2  0  3  1  2  2  0
 0  0  1  0  0  0  1  1  1  2  2  1  1  0  3  3  3  3  0  2  2  1  0  2  2  3  3  2  1  1  1  1  1  2  0
 0  0  0  1  0  1  1  0  3  2  0  0  0  1  3  2  1  3  1  1  3  3  3  2  1  3  1  2  0  3  2  3  3  1  2
 0  0  0  0  1  1  2  3  1  1  1  0  2  0  0  3  0  1  1  2  0  2  2  3  1  3  2  1  1  3  3  0  2  0  2
 0  0  0  0  0  2  0  2  2  2  0  2  2  0  2  2  2  0  2  2  2  2  2  2  0  0  2  2  0  0  2  0  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+114x^28+296x^30+323x^32+348x^34+290x^36+260x^38+242x^40+116x^42+52x^44+4x^46+2x^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 0.236 seconds.