The generator matrix

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

generates a code of length 58 over Z4 who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+110x^50+266x^52+335x^54+293x^56+235x^58+223x^60+188x^62+155x^64+118x^66+70x^68+37x^70+15x^72+1x^74+1x^76

The gray image is a code over GF(2) with n=116, k=11 and d=50.
This code was found by Heurico 1.16 in 0.507 seconds.