The generator matrix

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

generates a code of length 52 over Z4 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+82x^39+170x^40+316x^41+441x^42+648x^43+910x^44+1036x^45+1264x^46+1594x^47+1847x^48+2036x^49+2225x^50+2278x^51+2513x^52+2496x^53+2342x^54+2332x^55+1945x^56+1656x^57+1495x^58+1024x^59+649x^60+544x^61+352x^62+198x^63+132x^64+104x^65+63x^66+34x^67+23x^68+4x^69+10x^70+2x^71+1x^72+1x^76

The gray image is a code over GF(2) with n=104, k=15 and d=39.
This code was found by Heurico 1.10 in 40.8 seconds.