The generator matrix

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

generates a code of length 52 over Z4 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+76x^40+122x^41+245x^42+334x^43+462x^44+588x^45+716x^46+806x^47+846x^48+1064x^49+1038x^50+1128x^51+1286x^52+1250x^53+1191x^54+1114x^55+965x^56+806x^57+672x^58+544x^59+367x^60+280x^61+206x^62+96x^63+76x^64+48x^65+25x^66+10x^67+17x^68+2x^69+2x^70+1x^78

The gray image is a code over GF(2) with n=104, k=14 and d=40.
This code was found by Heurico 1.16 in 50.7 seconds.