The generator matrix

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

generates a code of length 56 over Z4 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+62x^45+142x^46+202x^47+256x^48+322x^49+446x^50+398x^51+424x^52+500x^53+502x^54+570x^55+538x^56+546x^57+566x^58+530x^59+454x^60+436x^61+399x^62+260x^63+185x^64+164x^65+100x^66+88x^67+58x^68+18x^69+19x^70+4x^72+1x^78+1x^86

The gray image is a code over GF(2) with n=112, k=13 and d=45.
This code was found by Heurico 1.16 in 7.93 seconds.