The generator matrix

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

generates a code of length 32 over Z4 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+344x^28+240x^30+59x^32+216x^36+144x^38+20x^40

The gray image is a code over GF(2) with n=64, k=10 and d=28.
This code was found by Heurico 1.16 in 66.8 seconds.