The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+60x^28+94x^29+89x^30+82x^31+81x^32+104x^33+77x^34+60x^35+62x^36+94x^37+71x^38+42x^39+46x^40+28x^41+15x^42+8x^43+6x^44+4x^46

The gray image is a code over GF(2) with n=68, k=10 and d=28.
This code was found by Heurico 1.10 in 0.031 seconds.