The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+58x^46+84x^47+150x^48+200x^49+225x^50+226x^51+259x^52+246x^53+270x^54+292x^55+239x^56+288x^57+198x^58+234x^59+206x^60+192x^61+190x^62+150x^63+127x^64+96x^65+73x^66+36x^67+39x^68+2x^69+10x^70+2x^71+3x^72

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 1.83 seconds.