The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+74x^45+150x^46+190x^47+264x^48+310x^49+417x^50+396x^51+404x^52+520x^53+588x^54+510x^55+484x^56+576x^57+604x^58+572x^59+394x^60+430x^61+395x^62+302x^63+201x^64+122x^65+129x^66+72x^67+32x^68+16x^69+18x^70+6x^71+8x^72+2x^74+2x^76+1x^78+2x^80

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 21.8 seconds.