The generator matrix

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

generates a code of length 57 over Z4 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+58x^45+157x^46+304x^47+411x^48+510x^49+595x^50+752x^51+846x^52+892x^53+993x^54+1046x^55+1091x^56+1072x^57+1127x^58+982x^59+992x^60+970x^61+816x^62+782x^63+611x^64+474x^65+362x^66+282x^67+141x^68+56x^69+46x^70+12x^71+2x^72+1x^108

The gray image is a code over GF(2) with n=114, k=14 and d=45.
This code was found by Heurico 1.10 in 11.7 seconds.