The generator matrix

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

generates a code of length 53 over Z4 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+104x^39+229x^40+410x^41+644x^42+862x^43+1178x^44+1532x^45+2094x^46+2634x^47+3093x^48+3676x^49+4109x^50+4542x^51+4832x^52+4952x^53+5000x^54+4880x^55+4476x^56+3734x^57+3220x^58+2694x^59+2026x^60+1480x^61+1078x^62+790x^63+488x^64+300x^65+205x^66+126x^67+52x^68+36x^69+28x^70+8x^71+9x^72+8x^73+6x^74

The gray image is a code over GF(2) with n=106, k=16 and d=39.
This code was found by Heurico 1.10 in 158 seconds.