The generator matrix

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

generates a code of length 52 over Z4 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+56x^52+4x^56+3x^64

The gray image is a code over GF(2) with n=104, k=6 and d=52.
This code was found by Heurico 1.16 in 0.0255 seconds.