The generator matrix

1 0 0 0 0 0 1 1 1 2 0 0 2 1 1 2 2 1 0 1 2 0 2 1 2 1 1 2 1 1 1 1 0 0 0 2 1 0 1 0 0 1 1 1 1 2 1 0 1 1 1 1
0 1 0 0 0 0 0 0 0 0 1 2 1 1 1 1 1 2 1 0 1 2 0 3 1 1 2 0 1 3 2 1 0 0 1 2 3 2 2 2 1 0 2 2 1 0 0 1 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 1 3 1 1 2 3 1 2 3 2 1 1 0 1 3 3 1 2 3 0 0 0 2 0 0 1 2 1 1 1 3 3 2 3 1 2 1 3 1 0 0
0 0 0 1 0 0 0 1 1 1 2 0 1 0 2 0 3 3 3 3 1 1 3 2 0 3 2 1 0 0 1 2 1 1 0 2 0 1 3 0 0 1 2 3 1 0 2 1 2 1 0 0
0 0 0 0 1 0 1 0 1 3 2 0 3 0 3 1 0 3 2 2 3 1 3 1 0 2 3 0 3 0 3 0 2 1 1 1 0 3 2 2 2 3 2 2 1 0 1 0 3 1 0 0
0 0 0 0 0 1 1 3 2 1 1 1 2 3 0 1 3 2 3 1 2 0 1 2 3 2 3 0 1 3 0 1 0 2 0 1 0 1 3 3 1 3 0 1 0 3 2 3 0 0 0 0
0 0 0 0 0 0 2 2 0 2 2 2 0 2 0 2 2 0 2 0 2 2 0 2 0 2 0 0 0 0 2 2 2 2 2 2 2 0 2 0 2 2 0 2 2 2 0 0 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+62x^40+236x^42+563x^44+708x^46+958x^48+1084x^50+1113x^52+974x^54+882x^56+770x^58+478x^60+234x^62+97x^64+22x^66+5x^68+4x^70+1x^76

The gray image is a code over GF(2) with n=104, k=13 and d=40.
This code was found by Heurico 1.10 in 2.66 seconds.