The generator matrix

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

generates a code of length 57 over Z4 who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+41x^50+74x^51+82x^52+96x^53+92x^54+86x^55+85x^56+60x^57+55x^58+68x^59+43x^60+42x^61+35x^62+42x^63+24x^64+20x^65+26x^66+14x^67+15x^68+2x^69+5x^70+4x^71+6x^72+4x^73+2x^74

The gray image is a code over GF(2) with n=114, k=10 and d=50.
This code was found by Heurico 1.10 in 0.047 seconds.