The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+78x^52+128x^53+221x^54+356x^55+493x^56+518x^57+656x^58+640x^59+735x^60+894x^61+938x^62+1014x^63+1035x^64+1032x^65+905x^66+1084x^67+958x^68+914x^69+751x^70+690x^71+679x^72+476x^73+396x^74+282x^75+205x^76+120x^77+97x^78+28x^79+40x^80+14x^81+3x^82+2x^83+1x^110

The gray image is a code over GF(2) with n=130, k=14 and d=52.
This code was found by Heurico 1.10 in 13.8 seconds.