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

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

Homogenous weight enumerator: w(x)=1x^0+18x^52+8x^54+4x^56+1x^72

The gray image is a code over GF(2) with n=104, k=5 and d=52.
This code was found by Heurico 1.16 in 0.0174 seconds.