The generator matrix

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

generates a code of length 56 over Z4 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+54x^46+72x^47+127x^48+200x^49+242x^50+244x^51+257x^52+270x^53+223x^54+278x^55+276x^56+246x^57+259x^58+242x^59+212x^60+218x^61+179x^62+166x^63+112x^64+74x^65+58x^66+18x^67+35x^68+16x^69+7x^70+4x^71+4x^72+1x^74+1x^78

The gray image is a code over GF(2) with n=112, k=12 and d=46.
This code was found by Heurico 1.16 in 1.92 seconds.