The generator matrix

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

generates a code of length 64 over Z4 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+14x^68+1x^72

The gray image is a code over GF(2) with n=128, k=4 and d=68.
This code was found by Heurico 1.16 in 0.0564 seconds.