The generator matrix

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

generates a code of length 62 over Z4 who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+174x^50+697x^52+1048x^54+1497x^56+1652x^58+1999x^60+2102x^62+2104x^64+1886x^66+1435x^68+980x^70+523x^72+208x^74+61x^76+14x^78+2x^80+1x^112

The gray image is a code over GF(2) with n=124, k=14 and d=50.
This code was found by Heurico 1.10 in 13.2 seconds.