The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+65x^40+130x^41+255x^42+342x^43+458x^44+574x^45+661x^46+820x^47+958x^48+994x^49+1065x^50+1146x^51+1219x^52+1298x^53+1178x^54+1108x^55+898x^56+836x^57+728x^58+506x^59+397x^60+284x^61+176x^62+96x^63+90x^64+40x^65+28x^66+14x^67+10x^68+4x^69+5x^70

The gray image is a code over GF(2) with n=104, k=14 and d=40.
This code was found by Heurico 1.10 in 10.3 seconds.