The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+110x^28+286x^30+334x^32+310x^34+368x^36+242x^38+230x^40+114x^42+42x^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 1.10 in 0.094 seconds.