The generator matrix

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

generates a code of length 58 over Z4 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+170x^52+188x^54+144x^56+146x^58+110x^60+74x^62+81x^64+52x^66+26x^68+14x^70+10x^72+6x^74+2x^76

The gray image is a code over GF(2) with n=116, k=10 and d=52.
This code was found by Heurico 1.10 in 1.06 seconds.