The generator matrix

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

generates a code of length 56 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+92x^44+122x^45+273x^46+408x^47+537x^48+642x^49+654x^50+754x^51+935x^52+1000x^53+1054x^54+1164x^55+1067x^56+1106x^57+1094x^58+1054x^59+944x^60+904x^61+723x^62+586x^63+436x^64+276x^65+268x^66+120x^67+77x^68+46x^69+29x^70+10x^71+7x^72+1x^102

The gray image is a code over GF(2) with n=112, k=14 and d=44.
This code was found by Heurico 1.16 in 58.2 seconds.