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

generates a code of length 52 over Z4 who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+92x^43+161x^44+192x^45+226x^46+240x^47+258x^48+242x^49+233x^50+258x^51+335x^52+268x^53+237x^54+280x^55+260x^56+216x^57+142x^58+128x^59+111x^60+100x^61+48x^62+24x^63+25x^64+6x^65+9x^66+2x^67+1x^68+1x^70

The gray image is a code over GF(2) with n=104, k=12 and d=43.
This code was found by Heurico 1.16 in 91.3 seconds.