The generator matrix

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

generates a code of length 52 over Z4 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+99x^38+158x^39+437x^40+606x^41+885x^42+1268x^43+1602x^44+1952x^45+2403x^46+3068x^47+3704x^48+4192x^49+4567x^50+4986x^51+4959x^52+5188x^53+4853x^54+4380x^55+3902x^56+3174x^57+2613x^58+1968x^59+1564x^60+1056x^61+721x^62+500x^63+299x^64+204x^65+93x^66+50x^67+43x^68+12x^69+20x^70+6x^71+1x^72+2x^74

The gray image is a code over GF(2) with n=104, k=16 and d=38.
This code was found by Heurico 1.10 in 153 seconds.