The generator matrix

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

generates a code of length 30 over Z4 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+24x^29+16x^30+15x^32+8x^33

The gray image is a code over GF(2) with n=60, k=6 and d=29.
This code was found by Heurico 1.10 in 0.047 seconds.