The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  2  2  0  0  2  2  0  0  2  2
 0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  2  2  0  0  2  2  0  2  2  2  2
 0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  0  2  2  0  0  2  2  2  2  0  0  0  0
 0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  0  2  2  0  0  0  0  2  2  0  2  0  2  0

generates a code of length 30 over Z4 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+15x^28+32x^30+15x^32+1x^60

The gray image is a code over GF(2) with n=60, k=6 and d=28.
This code was found by Heurico 1.16 in 0.00437 seconds.