The generator matrix

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

generates a code of length 53 over Z4 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+48x^41+173x^42+258x^43+337x^44+446x^45+608x^46+734x^47+779x^48+840x^49+1033x^50+1124x^51+1143x^52+1236x^53+1138x^54+1172x^55+1133x^56+990x^57+804x^58+638x^59+558x^60+376x^61+295x^62+214x^63+131x^64+90x^65+42x^66+20x^67+14x^68+6x^69+2x^70+1x^86

The gray image is a code over GF(2) with n=106, k=14 and d=41.
This code was found by Heurico 1.10 in 10.6 seconds.