The generator matrix

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

generates a code of length 64 over Z4 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+224x^52+736x^54+1006x^56+1366x^58+1796x^60+1914x^62+2197x^64+2124x^66+1819x^68+1376x^70+870x^72+586x^74+252x^76+86x^78+22x^80+4x^82+4x^84+1x^100

The gray image is a code over GF(2) with n=128, k=14 and d=52.
This code was found by Heurico 1.16 in 70.9 seconds.