The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+36x^38+76x^39+193x^40+350x^41+507x^42+614x^43+837x^44+1048x^45+1278x^46+1634x^47+1830x^48+2014x^49+2199x^50+2320x^51+2471x^52+2508x^53+2359x^54+2214x^55+1913x^56+1614x^57+1325x^58+1058x^59+743x^60+548x^61+416x^62+234x^63+183x^64+102x^65+57x^66+40x^67+21x^68+8x^69+15x^70+2x^71

The gray image is a code over GF(2) with n=104, k=15 and d=38.
This code was found by Heurico 1.10 in 39.5 seconds.