The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+46x^39+180x^40+314x^41+510x^42+666x^43+845x^44+1062x^45+1265x^46+1548x^47+1813x^48+1972x^49+2208x^50+2452x^51+2541x^52+2556x^53+2444x^54+2210x^55+1917x^56+1622x^57+1304x^58+1038x^59+708x^60+578x^61+393x^62+212x^63+158x^64+76x^65+64x^66+20x^67+25x^68+12x^69+2x^70+3x^72+2x^74+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 1.16 in 99 seconds.