The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+59x^32+4x^40

The gray image is a code over GF(2) with n=64, k=6 and d=32.
This code was found by Heurico 1.16 in 0.00478 seconds.