The generator matrix

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

generates a code of length 65 over Z4 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+100x^52+116x^53+261x^54+326x^55+428x^56+532x^57+627x^58+714x^59+765x^60+848x^61+884x^62+1062x^63+967x^64+1038x^65+1048x^66+988x^67+944x^68+962x^69+855x^70+684x^71+618x^72+478x^73+328x^74+268x^75+219x^76+114x^77+88x^78+48x^79+50x^80+8x^81+4x^82+6x^83+4x^84+1x^106

The gray image is a code over GF(2) with n=130, k=14 and d=52.
This code was found by Heurico 1.16 in 71.3 seconds.