The generator matrix

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

generates a code of length 34 over Z4 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+146x^30+77x^32+134x^34+30x^36+68x^38+18x^40+32x^42+2x^44+2x^46+2x^50

The gray image is a code over GF(2) with n=68, k=9 and d=30.
This code was found by Heurico 1.10 in 66 seconds.