The generator matrix

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

generates a code of length 32 over Z4 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+78x^26+201x^28+192x^30+182x^32+108x^34+121x^36+88x^38+37x^40+14x^42+2x^44

The gray image is a code over GF(2) with n=64, k=10 and d=26.
This code was found by Heurico 1.10 in 0.016 seconds.